Content-Type: multipart/mixed; boundary="-------------0202140301457" This is a multi-part message in MIME format. ---------------0202140301457 Content-Type: text/plain; name="02-66.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-66.keywords" Anderson localization, charge transport, electrical conductivity ---------------0202140301457 Content-Type: application/postscript; name="Chargetransport4.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Chargetransport4.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.66a p1.3 Copyright 1996-97 ASCII Corp.(www-ptex@ascii.co.jp) %% dvipsk 5.66a Copyright 1986-97 Radical Eye Software (www.radicaleye.com) %%Title: Chargetransport4.dvi %%Pages: 42 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips Chargetransport4.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.01.29:1120 %%BeginProcSet: texc.pro %! /TeXDict 250 dict def TeXDict begin 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2245 a(The) p 1595 2245 a(condition) p Fe 2000 2245 a(E) p Fh(j) p Fn(V) p Fj 2147 2259 a(!) p Fp 2197 2245 a(\(0\)) p Fh(j) p Fl 2337 2213 a(2) p Fn 2414 2245 a(<) p Fh 2521 2245 a(1) p Fp 2648 2245 a(is) p 2746 2245 a(assumed) p 3117 2245 a(in) p 3230 2245 a(order) 448 2370 y(that) p 645 2370 a(the) p 802 2370 a(Liouville) p 1174 2370 a(op) s(erator) p 1541 2370 a(of) p Fn 1645 2370 a(H) p Fm 1721 2384 a(E) p Fj 1764 2384 a(;!) p Fp 1863 2370 a(is) p 1955 2370 a(densely) p 2276 2370 a(de\014ned.) 589 2495 y @beginspecial @setspecial @endspecial(It) p 701 2495 a(is) p 806 2495 a(kno) m(wn) p 1107 2495 a(that,) p 1346 2495 a(the) p 1516 2495 a(sp) s(ectrum) p 1926 2495 a(of) p Fn 2043 2495 a(H) p Fj 2119 2509 a(!) p Fp 2213 2495 a(is) p 2318 2495 a(deterministic) p 2877 2495 a(almost) p 3184 2495 a(surely) p 3413 2495 a(,) 448 2619 y(and) p Fn 632 2619 a(\033) p Fp 687 2619 a(\() p Fn(H) p Fj 798 2633 a(!) p Fp 849 2619 a(\)) p 922 2619 a(=) p 1030 2619 a([) p Fh(\000) p Fp(2) p Fn(d;) p Fp 1258 2619 a(2) p Fn(d) p Fp(]) p 1402 2619 a(+) p 1498 2619 a(supp) p Fn 1715 2619 a(r) p Fp 1759 2619 a(,) p 1823 2619 a(for) p 1970 2619 a(a.e.) p Fn 2168 2619 a(!) p Fp 2228 2619 a([10) q(].) p 2457 2619 a(Moreo) m(v) m(er,) p 2891 2619 a(there) p 3131 2619 a(app) s(ears) 448 2744 y(some) p 690 2744 a(region) p 976 2744 a(in) p 1095 2744 a(the) p 1265 2744 a(sp) s(ectrum) p 1676 2744 a(dep) s(ending) p 2126 2744 a(on) p Fn 2266 2744 a(\025) p Fp 2363 2744 a(where) p 2639 2744 a(w) m(e) p 2786 2744 a(ha) m(v) m(e) p 3009 2744 a(pure) p 3230 2744 a(p) s(oin) m(t) 448 2868 y(sp) s(ectrum) p 850 2868 a(with) p 1061 2868 a(exp) s(onen) m(tially) p 1626 2868 a(deca) m(ying) p 2004 2868 a(eigenfunctions) p 2602 2868 a(whic) m(h,) p 2893 2868 a(as) p 3008 2868 a(w) m(e) p 3146 2868 a(already) 448 2993 y(men) m(tioned,) p 913 2993 a(is) p 1001 2993 a(a) p 1073 2993 a(mathematical) p 1640 2993 a(presen) m(tation) p 2156 2993 a(of) p 2256 2993 a(Anderson) p 2660 2993 a(lo) s(calization) p 3139 2993 a(\() p Fo(e.g.,) p Fp([1,) 448 3117 y(3) q(,) p 550 3117 a(9) q(,) p 652 3117 a(16) q(]\).) p 873 3117 a(In) p 987 3117 a([12) r(],) p 1186 3117 a(w) m(e) p 1321 3117 a(considered) p 1767 3117 a(the) p 1925 3117 a(c) m(harge) p 2211 3117 a(transp) s(ort) p 2615 3117 a(caused) p 2909 3117 a(b) m(y) p 3037 3117 a(the) p 3194 3117 a(slo) m(wly) 448 3242 y(v) p 491 3242 a(arying) p 775 3242 a(p) s(oten) m(tial.) p 1205 3242 a(W) p 1290 3242 a(e) p 1365 3242 a(used) p 1576 3242 a(adiabatic) p 1974 3242 a(appro) m(ximation,) p 2610 3242 a(and) p 2790 3242 a(pro) m(v) m(ed) p 3090 3242 a(that) p 3290 3242 a(this) 448 3366 y(quan) m(tit) m(y) p 815 3366 a(is) p 910 3366 a(equal) p 1153 3366 a(to) p 1267 3366 a(zero) p 1462 3366 a(almost) p 1759 3366 a(surely) p 2028 3366 a(when) p Fn 2268 3366 a(\025) p Fp 2355 3366 a(is) p 2450 3366 a(su\016cien) m(tly) p 2908 3366 a(large) p 3133 3366 a(\() p Fo(i.e.,) p Fp 3356 3366 a(at) 448 3491 y(high) p 656 3491 a(disorder\).) p 1093 3491 a(In) p 1212 3491 a(this) p 1394 3491 a(pap) s(er,) p 1682 3491 a(w) m(e) p 1821 3491 a(consider) p 2181 3491 a(the) p 2343 3491 a(c) m(harge) p 2634 3491 a(transp) s(ort) p 3042 3491 a(caused) p 3341 3491 a(b) m(y) 448 3615 y(the) p 605 3615 a(discrete) p 939 3615 a(analogue) p 1318 3615 a(of) p 1421 3615 a(the) p 1578 3615 a(constan) m(t) p 1945 3615 a(electric) p 2258 3615 a(\014eld) p Fh 2455 3615 a(E) p Fp 2511 3615 a(\() p Fh(2) p Fp 2632 3615 a(I) p 2650 3615 a(R\)) p Fn 1537 3787 a(H) p Fj 1613 3801 a(!) r(;) p Fm(E) p Fp 1751 3787 a(:=) p Fn 1872 3787 a(H) p Fj 1948 3801 a(!) p Fp 2019 3787 a(+) p Fh 2110 3787 a(E) p 2186 3787 a(\001) p Fn 2231 3787 a(x) p Fl 2283 3801 a(1) p Fn 2323 3787 a(;) p Fp 448 3787 a(\(1.2\)) 448 3958 y @beginspecial @setspecial @endspecial(where) p Fn 711 3958 a(x) p Fl 763 3972 a(1) p Fp 833 3958 a(is) p 925 3958 a(the) p 1081 3958 a(\014rst) p 1269 3958 a(comp) s(onen) m(t) p 1734 3958 a(of) p Fn 1837 3958 a(x) p Fp 1915 3958 a(=) p 2011 3958 a(\() p Fn(x) p Fl 2098 3972 a(1) p Fn 2137 3958 a(;) p 2177 3958 a(x) p Fl 2229 3972 a(2) p Fn 2269 3958 a(;) p Fh 2309 3958 a(\001) p 2349 3958 a(\001) p 2389 3958 a(\001) p Fn 2431 3958 a(;) p 2471 3958 a(x) p Fj 2523 3973 a(d) p Fp 2564 3958 a(\)) p Fh 2624 3958 a(2) p Fk 2710 3958 a(Z) p 2730 3958 a(Z) p Fj 2785 3922 a(d) p Fp 2826 3958 a(.) p 2891 3958 a(W) p 2976 3958 a(e) p 3048 3958 a(de\014ne) p 3311 3958 a(the) 448 4083 y(c) m(harge) p 729 4083 a(transp) s(ort) p 1126 4083 a(b) m(y) p 1247 4083 a(carrying) p 1598 4083 a(out) p 1754 4083 a(the) p 1905 4083 a(follo) m(wing) p 2284 4083 a(three) p 2511 4083 a(op) s(erations) p 2948 4083 a(successiv) m(ely:) 448 4208 y(\(1\)) p 601 4208 a(tak) m(e) p 805 4208 a(the) p 968 4208 a(thermal) p 1314 4208 a(a) m(v) m(erage) p 1646 4208 a(of) p 1756 4208 a(curren) m(t) p 2079 4208 a(op) s(erator) p 2453 4208 a(at) p 2570 4208 a(zero) p 2769 4208 a(temp) s(erature,) p 3321 4208 a(\(2\)) 448 4332 y(divide) p 719 4332 a(it) p 809 4332 a(b) m(y) p Fh 936 4332 a(E) p Fp 1022 4332 a(and) p 1199 4332 a(let) p Fh 1330 4332 a(E) p 1412 4332 a(#) p Fp 1482 4332 a(0,) p 1583 4332 a(\(3\)) p 1730 4332 a(tak) m(e) p 1927 4332 a(the) p 2083 4332 a(time) p 2290 4332 a(a) m(v) m(erage.) p 2652 4332 a(That) p 2879 4332 a(is,) p Fn 754 4544 a(\033) p Fl 806 4558 a(1) p Fp 845 4544 a(\() p Fn(!) s(;) p 980 4544 a(\017) p Fj 1017 4558 a(F) p Fp 1077 4544 a(\)) p 1137 4544 a(:=) p 1274 4544 a(lim) p Fj 1258 4604 a(T) p Fm 1309 4604 a("1) p Fi 1430 4429 a(Z) p Fj 1513 4456 a(T) p Fl 1476 4618 a(0) p Fn 1593 4483 a(dt) p 1593 4523 81 4 v 1600 4607 a(T) p Fp 1699 4544 a(lim) p Fm 1705 4604 a(E) p 1748 4604 a(#) p Fl(0) p Fp 1855 4483 a(1) p 1850 4523 57 4 v Fh 1850 4607 a(E) 1916 4544 y(T) p Fp 1989 4544 a(\() p Fn(e) p Fj 2066 4507 a(itH) p Ff 2173 4518 a(!) r(;) p Fd(E) p Fn 2279 4544 a(i) p Fp([) p Fn(H) p Fj 2411 4558 a(!) p Fn 2462 4544 a(;) p 2502 4544 a(x) p Fl 2554 4558 a(1) p Fp 2594 4544 a(]) p Fn(e) p Fm 2661 4507 a(\000) p Fj(itH) p Ff 2823 4518 a(!) r(;) p Fd(E) p Fn 2929 4544 a(P) p Fj 2987 4558 a(\017) p Ff 3016 4569 a(F) p Fp 3071 4544 a(\)) p Fn(;) p Fp 448 4544 a(\(1.3\)) 448 4744 y @beginspecial @setspecial @endspecial(where) p Fh 711 4744 a(T) p Fp 814 4744 a(is) p 906 4744 a(the) p 1062 4744 a(trace) p 1290 4744 a(p) s(er) p 1449 4744 a(v) m(olume) p 1762 4744 a(for) p 1901 4744 a(an) p 2028 4744 a(op) s(erator) p Fn 2394 4744 a(A) p Fp(:) p Fh 1242 4937 a(T) p Fp 1314 4937 a(\() p Fn(A) p Fp(\)) p 1479 4937 a(:=) p 1614 4937 a(lim) p Fj 1600 4997 a(L) p Fm("1) p Fp 1839 4875 a(1) p 1779 4916 166 4 v Fh 1779 4999 a(j) p Fp(\003) p Fj 1867 5013 a(L) p Fh 1919 4999 a(j) p Fp 1955 4937 a(trace) q(\() p Fn(\037) p Fl 2244 4951 a(\003) p Ff 2293 4962 a(L) p Fn 2343 4937 a(A) p 2426 4937 a(\037) p Fl 2483 4951 a(\003) p Ff 2532 4962 a(L) p Fp 2583 4937 a(\)) p Fn(:) p Fp 448 4937 a(\(1.4\)) 1920 5225 y(2) p eop %%Page: 3 3 3 2 bop Fn 448 573 a(\037) p Fj 505 587 a(C) p Fp 595 573 a(is) p 686 573 a(the) p 843 573 a(c) m(haracteristic) p 1402 573 a(fun) m(tion) p 1715 573 a(of) p 1818 573 a(a) p 1894 573 a(set) p Fn 2036 573 a(C) p Fp 2108 573 a(,) p 2163 573 a(and) p 2340 573 a(\003) p Fj 2403 587 a(L) p Fp 2485 573 a(is) p 2577 573 a(a) p 2653 573 a(\014nite) p 2885 573 a(b) s(o) m(x) p 3059 573 a(in) p Fk 3165 573 a(Z) p 3185 573 a(Z) p Fj 3240 536 a(d) p Fp 3280 573 a(:) 1166 789 y(\003) p Fj 1229 803 a(L) p Fp 1307 789 a(:=) p Fh 1428 789 a(f) p Fn(x) p Fh 1551 789 a(2) p Fk 1636 789 a(Z) p 1656 789 a(Z) p Fj 1711 751 a(d) p Fp 1777 789 a(:) p Fh 1827 789 a(j) p Fn(x) p Fj 1904 803 a(j) p Fh 1941 789 a(j) p 1992 789 a(\024) p Fn 2088 789 a(L;) p 2190 789 a(j) p Fp 2258 789 a(=) p 2354 789 a(1) p Fn(;) p Fh 2439 789 a(\001) p 2479 789 a(\001) p 2519 789 a(\001) p Fn 2561 789 a(;) p 2601 789 a(d) p Fh(g) p Fn(:) 448 1005 y(e) p Fm 490 972 a(\000) p Fj(itH) p Ff 652 983 a(!) r(;) p Fd(E) p Fp 789 1005 a(is) p 882 1005 a(the) p 1039 1005 a(unitary) p 1361 1005 a(propagator) p 1826 1005 a(of) p Fn 1931 1005 a(H) p Fj 2007 1019 a(!) r(;) p Fm(E) p Fp 2119 1005 a(,) p 2176 1005 a(and) p Fn 2353 1005 a(P) p Fj 2411 1019 a(\017) p Ff 2440 1030 a(F) p Fp 2526 1005 a(is) p 2618 1005 a(the) p 2776 1005 a(F) p 2827 1005 a(ermi) p 3035 1005 a(pro) p 3172 1005 a(jection) 448 1129 y(op) s(erator:) p Fn 858 1129 a(\037) p Fl 915 1148 a(\() p Fm(\0001) p Fj(;\017) p Ff 1117 1159 a(F) p Fl 1167 1148 a(]) p Fp 1191 1129 a(\() p Fn(H) p Fj 1302 1143 a(!) p Fp 1352 1129 a(\),) p 1448 1129 a(corresp) s(onding) p 2036 1129 a(to) p 2151 1129 a(the) p 2311 1129 a(F) p 2362 1129 a(ermi) p 2574 1129 a(energy) p Fn 2869 1129 a(\017) p Fj 2906 1143 a(F) p Fh 2996 1129 a(2) p Fp 3089 1129 a(I) p 3107 1129 a(R) p 3207 1129 a(whic) m(h) 448 1254 y(w) m(e) p 585 1254 a(\014x) p 717 1254 a(arbitrary) p 1067 1254 a(.) p 1141 1254 a(In) p 1258 1254 a(the) p 1417 1254 a(de\014nition) p 1824 1254 a(of) p Fn 1931 1254 a(\033) p Fl 1983 1268 a(1) p Fp 2022 1254 a(\() p Fn(!) s(;) p 2157 1254 a(\017) p Fj 2194 1268 a(F) p Fp 2253 1254 a(\),) p 2348 1254 a(it) p 2442 1254 a(migh) m(t) p 2705 1254 a(b) s(e) p 2832 1254 a(more) p 3063 1254 a(natural) p 3384 1254 a(if) 448 1378 y(w) m(e) p 585 1378 a(to) s(ok) p 796 1378 a(lim) p Fm 922 1393 a(E) p 965 1393 a(#) p Fl(0) 1069 1342 y(1) p 1065 1357 43 4 v Fm 1065 1410 a(E) p Fp 1151 1378 a(after) p 1370 1378 a(taking) p 1653 1378 a(the) p 1813 1378 a(time) p 2023 1378 a(a) m(v) m(erage) p 2353 1378 a(lim) p Fj 2479 1393 a(T) p Fm 2530 1393 a("1) p Fi 2655 1309 a(R) p Fj 2710 1336 a(T) p Fl 2694 1406 a(0) p Fj 2791 1342 a(dt) p 2791 1357 62 4 v 2796 1410 a(T) p Fp 2862 1378 a(.) p 2938 1378 a(Ho) m(w) m(ev) m(er,) p 3334 1378 a(w) m(e) 448 1503 y(can) p 618 1503 a(only) p 820 1503 a(deal) p 1015 1503 a(with) p 1225 1503 a(the) p 1384 1503 a(Ab) s(el) p 1604 1503 a(limit) p 1824 1503 a(of) p 1930 1503 a(that,) p 2156 1503 a(whic) m(h) p 2419 1503 a(can) p 2588 1503 a(b) s(e) p 2715 1503 a(regarded) p 3092 1503 a(as) p 3206 1503 a(a) p 3285 1503 a(sort) 448 1627 y(of) p 552 1627 a(appro) m(ximation.) p Fn 660 1865 a(\033) p Fl 712 1879 a(2) p Fp 751 1865 a(\() p Fn(!) s(;) p 886 1865 a(\017) p Fj 923 1879 a(F) p Fp 982 1865 a(\)) p 1043 1865 a(:=) p 1164 1865 a(lim) p Fj 1175 1925 a(\016) p Fm 1208 1925 a(#) p Fl(0) p Fp 1305 1865 a(lim) p Fm 1312 1925 a(E) p 1355 1925 a(#) p Fl(0) p Fp 1462 1803 a(1) p 1457 1844 57 4 v Fh 1457 1927 a(E) p Fi 1538 1750 a(Z) p Fm 1621 1776 a(1) p Fl 1584 1938 a(0) p Fn 1711 1865 a(dt) p 1806 1865 a(\016) s(e) p Fm 1891 1827 a(\000) p Fj(t\016) p Fh 2011 1865 a(T) p Fp 2083 1865 a(\() p Fn(e) p Fj 2160 1827 a(itH) p Ff 2267 1838 a(!) r(;) p Fd(E) p Fn 2374 1865 a(i) p Fp([) p Fn(H) p Fj 2506 1879 a(!) p Fn 2556 1865 a(;) p 2596 1865 a(x) p Fl 2648 1879 a(1) p Fp 2688 1865 a(]) p Fn(e) p Fm 2755 1827 a(\000) p Fj(itH) p Ff 2917 1838 a(!) r(;) p Fd(E) p Fn 3023 1865 a(P) p Fj 3081 1879 a(\017) p Ff 3110 1890 a(F) p Fp 3165 1865 a(\)) p Fn(;) p Fp 448 1865 a(\(1.5\)) p Fe 448 2114 a(Remark) p 846 2114 a(1.1) p 1025 2114 a @beginspecial @setspecial @endspecial Fo(\(1\)) p Fn 1171 2114 a(\033) p Fl 1223 2128 a(1) p Fp 1263 2114 a(\() p Fn(!) s(;) p 1398 2114 a(\017) p Fj 1435 2128 a(F) p Fp 1494 2114 a(\)) p Fo 1555 2114 a(was) p 1725 2114 a(original) p 2032 2114 a(ly) p 2126 2114 a(de\014ne) p 2353 2114 a(d) p 2426 2114 a(in) p 2530 2114 a([8) q(].) p 2700 2114 a(Inste) p 2890 2114 a(ad) p 3009 2114 a(of) p 3110 2114 a(studying) p Fn 448 2238 a(\033) p Fl 500 2252 a(1) p Fp 540 2238 a(\() p Fn(!) s(;) p 675 2238 a(\017) p Fj 712 2252 a(F) p Fp 771 2238 a(\)) p Fo(,) p 867 2238 a(they) p 1063 2238 a(c) p 1100 2238 a(ompute) p 1382 2238 a(d) p Fn 1463 2238 a(\033) p Fl 1515 2252 a(2) p Fp 1554 2238 a(\() p Fn(!) s(;) p 1689 2238 a(\017) p Fj 1726 2252 a(F) p Fp 1786 2238 a(\)) p Fo 1854 2238 a(by) p 1973 2238 a(using) p 2213 2238 a(the) p 2364 2238 a(r) p 2397 2238 a(elaxation) p 2787 2238 a(time) p 2994 2238 a(appr) p 3165 2238 a(oxima-) 448 2363 y(tion.) 589 2487 y @beginspecial @setspecial @endspecial(\(2\)) p 737 2487 a(We) p 896 2487 a(ar) p 975 2487 a(e) p 1044 2487 a(not) p 1199 2487 a(able) p 1378 2487 a(to) p 1481 2487 a(discuss) p 1784 2487 a(the) p 1929 2487 a(de) p 2012 2487 a(ep) p 2128 2487 a(question) p 2480 2487 a(that) p 2659 2487 a(whether) p 2991 2487 a(the) p 3136 2487 a(discr) p 3322 2487 a(ete) 448 2612 y(analo) p 655 2612 a(gue) p 819 2612 a(of) p 923 2612 a(the) p 1071 2612 a(c) p 1108 2612 a(onstant) p 1430 2612 a(ele) p 1532 2612 a(ctric) p 1742 2612 a(\014eld) p Fh 1934 2612 a(E) p 2003 2612 a(\001) p Fn 2041 2612 a(x) p Fl 2093 2626 a(1) p Fo 2163 2612 a(would) p 2417 2612 a(b) p 2454 2612 a(e) p 2526 2612 a(appr) p 2697 2612 a(opriate) p 3006 2612 a(to) p 3112 2612 a(c) p 3149 2612 a(ompute) 448 2736 y(the) p 598 2736 a(ele) p 700 2736 a(ctric) p 875 2736 a(al) p 976 2736 a(c) p 1013 2736 a(onductivity) p 1481 2736 a([7) q(,) p 1614 2736 a(15) q(].) p 1804 2736 a(In) p 1922 2736 a(fact,) p 2127 2736 a(the) p 2277 2736 a(sp) p 2355 2736 a(e) p 2392 2736 a(ctrum) p 2657 2736 a(of) p Fn 2763 2736 a(H) p Fj 2839 2750 a(!) r(;) p Fm(E) p Fo 2982 2736 a(is) p 3078 2736 a(known) p 3360 2736 a(to) 448 2861 y(b) p 485 2861 a(e) p 565 2861 a(pur) p 693 2861 a(ely) p 841 2861 a(discr) p 1027 2861 a(ete.) p 1228 2861 a(However,) p 1633 2861 a(we) p 1774 2861 a(b) p 1811 2861 a(elieve) p 2067 2861 a(that) p 2258 2861 a(taking) p Fh 2536 2861 a(E) p 2627 2861 a(#) p Fp 2707 2861 a(0) p Fo 2791 2861 a(limit) p Fp 3012 2861 a(lim) p Fm 3138 2876 a(E) p 3181 2876 a(#) p Fl(0) 3285 2825 y(1) p 3281 2840 43 4 v Fm 3281 2892 a(E) p Fo 3372 2861 a(is) 448 2985 y(not) p 609 2985 a(trivial) p 877 2985 a(in) p 988 2985 a(any) p 1163 2985 a(c) p 1200 2985 a(ase.) 589 3110 y @beginspecial @setspecial @endspecial(\(3\)) p 739 3110 a(In) p 853 3110 a(non-zer) p 1146 3110 a(o) p 1222 3110 a(temp) p 1409 3110 a(er) p 1484 3110 a(atur) p 1642 3110 a(e,) p Fn 1744 3110 a(P) p Fj 1802 3124 a(\017) p Ff 1831 3135 a(F) p Fo 1914 3110 a(is) p 2007 3110 a(r) p 2040 3110 a(eplac) p 2234 3110 a(e) p 2271 3110 a(d) p 2348 3110 a(by) p Fn 2463 3110 a(f) p Fj 2508 3125 a(\014) s(;\017) p Ff 2600 3136 a(F) p Fp 2653 3110 a(\() p Fn(H) p Fj 2764 3124 a(!) p Fp 2815 3110 a(\)) p Fo(,) p 2907 3110 a(wher) p 3088 3110 a(e) p Fn 3160 3110 a(f) p Fj 3205 3125 a(\014) s(;\026) p Fp 3313 3110 a(\() p Fn(\025) p Fp(\)) p Fo 448 3234 a(is) p 546 3234 a(the) p 697 3234 a(F) p 749 3234 a(ermi-Dir) p 1094 3234 a(ac) p 1215 3234 a(distribution) p 1702 3234 a(function) p Fn 1084 3466 a(f) p Fj 1129 3481 a(\014) s(;\026) p Fp 1238 3466 a(\() p Fn(\025) p Fp(\)) p 1387 3466 a(:=) p Fi 1508 3372 a(\020) p Fp 1558 3466 a(1) p 1624 3466 a(+) p 1715 3466 a(exp) o([) p Fn(\014) p Fp 1934 3466 a(\() p Fn(\025) p Fh 2043 3466 a(\000) p Fn 2134 3466 a(\026) p Fp(\)]) p Fi 2249 3372 a(\021) p Fm 2299 3395 a(\000) p Fl(1) p Fn 2394 3466 a(;) p 2527 3466 a(\025) p Fh 2605 3466 a(2) p Fp 2691 3466 a(I) p 2709 3466 a(R) p Fn(;) 448 3682 y @beginspecial @setspecial @endspecial Fo(and) p Fn 625 3682 a(\014) p 706 3682 a(>) p Fp 802 3682 a(0) p Fo 880 3682 a(is) p 978 3682 a(the) p 1129 3682 a(inverse) p 1441 3682 a(temp) p 1628 3682 a(er) p 1703 3682 a(atur) p 1861 3682 a(e.) 448 3881 y @beginspecial @setspecial @endspecial Fp(Throughout) p 960 3881 a(this) p 1143 3881 a(pap) s(er,) p 1431 3881 a(w) m(e) p 1571 3881 a(assume) p 1891 3881 a(the) p 2054 3881 a(follo) m(wing) p 2444 3881 a(deca) m(ying) p 2823 3881 a(prop) s(ert) m(y) p 3201 3881 a(of) p 3311 3881 a(the) 448 4005 y(matrix) p 744 4005 a(elemen) m(t) p 1080 4005 a(of) p 1183 4005 a(the) p 1340 4005 a(F) p 1391 4005 a(ermi) p 1599 4005 a(pro) p 1736 4005 a(jection.) 448 4221 y @beginspecial @setspecial @endspecial Fe(Assumption) 1333 4345 y(E) p Fi 1430 4264 a(X) p Fj 1417 4449 a(x) p Fm(2) p Fg(Z) p 1520 4449 a(Z) p Fh 1578 4345 a(j) p Fn(x) p Fl 1655 4359 a(1) p Fh 1695 4345 a(j) p Fl 1720 4308 a(2) p Fh 1759 4345 a(j) p Fn(P) p Fj 1842 4359 a(\017) p Ff 1871 4370 a(F) p Fp 1926 4345 a(\() p Fn(!) p Fp 2037 4345 a(;) p Fn 2077 4345 a(x;) p Fp 2169 4345 a(0\)) p Fh(j) p Fl 2274 4308 a(2) p Fn 2340 4345 a(<) p Fh 2436 4345 a(1) p Fn(:) p Fp 448 4345 a(\(1.6\)) 589 4683 y @beginspecial @setspecial @endspecial Fn(P) p Fj 647 4697 a(\017) p Ff 676 4708 a(F) p Fp 731 4683 a(\() p Fn(!) p Fp 842 4683 a(;) p Fn 882 4683 a(x;) p 974 4683 a(y) p Fp 1022 4683 a(\)) p 1106 4683 a(:=) p Fn(<) p 1320 4683 a(\016) p Fj 1360 4697 a(x) p Fn 1404 4683 a(;) p 1444 4683 a(P) p Fj 1502 4697 a(\017) p Ff 1531 4708 a(F) p Fn 1587 4683 a(\016) p Fj 1627 4697 a(y) p Fn 1716 4683 a(>) p Fj 1787 4712 a(l) p Fc 1809 4693 a(2) p Fl 1844 4712 a(\() p Fg(Z) p 1887 4712 a(Z) p Ff 1930 4686 a(d) p Fl 1966 4712 a(\)) p Fp 1998 4683 a(,) p 2070 4683 a(where) p Fn 2347 4683 a(<) p Fh 2465 4683 a(\001) p Fn 2505 4683 a(;) p Fh 2561 4683 a(\001) p Fn 2634 4683 a(>) p Fj 2705 4712 a(l) p Fc 2727 4693 a(2) p Fl 2762 4712 a(\() p Fg(Z) p 2805 4712 a(Z) p Ff 2848 4686 a(d) p Fl 2884 4712 a(\)) p Fp 2960 4683 a(is) p 3065 4683 a(the) p 3235 4683 a(inner) 448 4820 y(pro) s(duct) p 797 4820 a(on) p Fn 932 4820 a(l) p Fl 961 4787 a(2) p Fp 1000 4820 a(\() p Fk(Z) p 1055 4820 a(Z) p Fj 1110 4783 a(d) p Fp 1150 4820 a(\),) p 1251 4820 a(and) p Fn 1436 4820 a(\016) p Fj 1476 4834 a(x) p Fp 1520 4820 a(\() p Fn(z) p Fp 1601 4820 a(\)) p 1676 4820 a(=) p 1785 4820 a(1,) p 1896 4820 a(if) p Fn 1987 4820 a(z) p Fp 2072 4820 a(=) p Fn 2181 4820 a(x) p Fp(,) p 2298 4820 a(and) p Fn 2483 4820 a(\016) p Fj 2523 4834 a(x) p Fp 2567 4820 a(\() p Fn(z) p Fp 2648 4820 a(\)) p 2722 4820 a(=) p 2832 4820 a(0,) p 2943 4820 a(if) p Fn 3034 4820 a(z) p Fh 3118 4820 a(6) p Fp(=) p Fn 3228 4820 a(x) p Fp(.) p 3369 4820 a(It) 1920 5225 y(3) p eop %%Page: 4 4 4 3 bop Fp 448 573 a(is) p 549 573 a(sho) m(wn) p 835 573 a(that) p 1041 573 a([2) q(],) p 1205 573 a(\(1.6\)) p 1432 573 a(follo) m(ws) p 1740 573 a(from) p 1964 573 a(the) p 2131 573 a(fractional) p 2547 573 a(momen) m(t) p 2908 573 a(b) s(ound) p 3198 573 a(of) p 3311 573 a(the) 448 697 y(Green's) p 778 697 a(function) p Fe 1042 897 a(E) p Fh(j) p Fn(G) p Fj 1208 911 a(\017) p Ff 1237 922 a(F) p Fl 1287 911 a(+) p Fj(i\017) p Fp 1399 897 a(\() p Fn(!) p Fp 1509 897 a(;) p Fn 1549 897 a(x;) p 1641 897 a(y) p Fp 1689 897 a(\)) p Fh(j) p Fj 1749 859 a(s) p Fh 1812 897 a(\024) p Fn 1908 897 a(C) p 1980 897 a(e) p Fm 2022 859 a(\000) p Fj(\026) p Fm(j) p Fj(x) p Fm(\000) p Fj(y) p Fm 2271 859 a(j) p Fn 2295 897 a(;) p 2426 897 a(x;) p 2544 897 a(y) p Fh 2617 897 a(2) p Fk 2703 897 a(Z) p 2723 897 a(Z) p Fj 2777 859 a(d) p Fn 2818 897 a(;) p Fp 448 897 a(\(1.7\)) 448 1096 y @beginspecial @setspecial @endspecial(for) p 598 1096 a(some) p 837 1096 a(constan) m(ts) p 1250 1096 a(0) p Fn 1338 1096 a(<) p 1452 1096 a(s) p 1538 1096 a(<) p Fp 1651 1096 a(1,) p Fn 1766 1096 a(C) p 1880 1096 a(>) p Fp 1994 1096 a(0,) p Fn 2108 1096 a(\026) p 2206 1096 a(>) p Fp 2320 1096 a(0,) p 2434 1096 a(uniformly) p 2859 1096 a(w.r.t.) p Fn 3144 1096 a(\017) p Fh 3224 1096 a(2) p Fp 3327 1096 a(I) p 3345 1096 a(R.) p Fn 448 1221 a(G) p Fj 520 1235 a(E) p Fp 579 1221 a(\() p Fn(!) p Fp 690 1221 a(;) p Fn 730 1221 a(x;) p 822 1221 a(y) p Fp 870 1221 a(\)) p 933 1221 a(:=) p Fn(<) p 1127 1221 a(\016) p Fj 1167 1235 a(x) p Fn 1211 1221 a(;) p Fp 1251 1221 a(\() p Fn(H) p Fj 1362 1235 a(!) p Fh 1434 1221 a(\000) p Fn 1525 1221 a(E) p Fp 1597 1221 a(\)) p Fm 1632 1188 a(\000) p Fl(1) p Fn 1727 1221 a(\016) p Fj 1767 1235 a(y) p Fn 1836 1221 a(>) p Fj 1907 1250 a(l) p Fc 1929 1231 a(2) p Fl 1963 1250 a(\() p Fg(Z) p 2006 1250 a(Z) p Ff 2050 1224 a(d) p Fl 2086 1250 a(\)) p Fp 2149 1221 a(is) p 2242 1221 a(the) p 2399 1221 a(matrix) p 2696 1221 a(elemen) m(t) p 3033 1221 a(of) p 3138 1221 a(Green's) 448 1346 y(function.) p 840 1346 a(\(1.7\)) p 1057 1346 a(is) p 1148 1346 a(one) p 1315 1346 a(of) p 1418 1346 a(the) p 1575 1346 a(k) m(ey) p 1739 1346 a(observ) p 1990 1346 a(ation) p 2222 1346 a(of) p 2325 1346 a(Anderson) p 2733 1346 a(lo) s(calization) p 3215 1346 a([1) q(,) p 3341 1346 a(3) q(],) 448 1470 y(and) p 628 1470 a(kno) m(wn) p 918 1470 a(to) p 1032 1470 a(hold) p 1236 1470 a(if) p 1322 1470 a(\(1\)) p Fn 1471 1470 a(\025) p 1553 1470 a(>) p Fp 1653 1470 a(0) p 1732 1470 a(is) p 1826 1470 a(su\016cien) m(tly) p 2283 1470 a(large) p 2508 1470 a(\(high) p 2748 1470 a(disorder) p 3100 1470 a(case\),) p 3356 1470 a(or) 448 1595 y(\(2\)) p Fh 601 1595 a(j) p Fn(\017) p Fj 663 1609 a(F) p Fh 722 1595 a(j) p Fp 784 1595 a(is) p 882 1595 a(su\016cien) m(tly) p 1343 1595 a(large) p 1572 1595 a(\(extreme) p 1960 1595 a(energy) p 2257 1595 a(case\),) p 2518 1595 a(or) p 2636 1595 a(\(3\)) p Fn 2789 1595 a(\017) p Fj 2826 1609 a(F) p Fp 2921 1595 a(is) p 3019 1595 a(a) m(w) m(a) m(y) p 3253 1595 a(from) 448 1719 y(the) p 601 1719 a(sp) s(ectrum) p 994 1719 a(of) p 1093 1719 a(free) p 1264 1719 a(Laplacian) p 1675 1719 a(for) p Fh 1810 1719 a(j) p Fn(\025) p Fh(j) p Fp 1940 1719 a(small) p 2174 1719 a(\(w) m(eak) p 2432 1719 a(disorder) p 2778 1719 a(case\).) p 3039 1719 a(Under) p 3311 1719 a(the) 448 1844 y(ab) s(o) m(v) m(e) p 706 1844 a(assumption\(1.6\),) p 1399 1844 a(w) m(e) p 1533 1844 a(ha) m(v) m(e) p 1742 1844 a(follo) m(wing) p 2126 1844 a(results.) 448 2059 y @beginspecial @setspecial @endspecial Fe(Theorem) p 892 2059 a(1) p Fn 1000 2059 a(\033) p Fl 1052 2073 a(2) p Fp 1091 2059 a(\() p Fn(!) s(;) p 1226 2059 a(\017) p Fj 1263 2073 a(F) p Fp 1323 2059 a(\)) p 1383 2059 a(=) p 1479 2059 a(0) p Fn(;) p 1656 2059 a(a:e:) p 1822 2059 a(!) s(:) 448 2275 y @beginspecial @setspecial @endspecial Fe(Theorem) p 892 2275 a(2) p Fn 1000 2275 a(\033) p Fl 1052 2289 a(1) p Fp 1091 2275 a(\() p Fn(!) s(;) p 1226 2275 a(\017) p Fj 1263 2289 a(F) p Fp 1323 2275 a(\)) p 1383 2275 a(=) p 1479 2275 a(0) p Fn(;) p 1656 2275 a(a:e:) p 1822 2275 a(!) s(:) p Fe 448 2460 a(Remark) p 846 2460 a(1.2) p 1025 2460 a @beginspecial @setspecial @endspecial Fo(\(1\)) p 1188 2460 a(We) p 1364 2460 a(c) p 1401 2460 a(an) p 1542 2460 a(extend) p 1838 2460 a(The) p 1986 2460 a(or) p 2065 2460 a(em) p 2226 2460 a(2) p 2315 2460 a(to) p 2435 2460 a(some) p 2678 2460 a(long-r) p 2906 2460 a(ange) p 3130 2460 a(hopping) 448 2585 y(Hamiltonians.) p 1047 2585 a(However,) p 1443 2585 a(it) p 1530 2585 a(se) p 1604 2585 a(ems) p 1788 2585 a(not) p 1945 2585 a(to) p 2051 2585 a(b) p 2088 2585 a(e) p 2159 2585 a(a) p 2235 2585 a(trivial) p 2500 2585 a(task) p 2685 2585 a(to) p 2791 2585 a(extend) p 3074 2585 a(the) p 3222 2585 a(r) p 3255 2585 a(esol-) 448 2709 y(vent) p 651 2709 a(e) p 688 2709 a(quation) p 1018 2709 a(\(Pr) p 1150 2709 a(op) p 1237 2709 a(osition) p 1543 2709 a(3.1\)) p 1738 2709 a(to) p 1852 2709 a(those) p 2091 2709 a(Hamiltonians,) p 2688 2709 a(which) p 2948 2709 a(is) p 3050 2709 a(imp) p 3193 2709 a(ortant) 448 2834 y(to) p 558 2834 a(pr) p 637 2834 a(ove) p 800 2834 a(The) p 948 2834 a(or) p 1027 2834 a(em) p 1178 2834 a(1.) 589 2958 y @beginspecial @setspecial @endspecial(\(2\)) p 736 2958 a(It) p 827 2958 a(would) p 1078 2958 a(r) p 1111 2958 a(e) p 1148 2958 a(quir) p 1300 2958 a(e) p 1368 2958 a(further) p 1666 2958 a(studies) p 1961 2958 a(to) p 2063 2958 a(se) p 2137 2958 a(e) p 2205 2958 a(under) p 2457 2958 a(which) p 2706 2958 a(c) p 2743 2958 a(onditions) p 3134 2958 a(the) p 3278 2958 a(var-) 448 3083 y(ious) p 645 3083 a(limits) p 902 3083 a(involve) p 1171 3083 a(d) p 1254 3083 a(in) p 1369 3083 a(the) p 1524 3083 a(de\014nitions) p 1971 3083 a(of) p Fn 2082 3083 a(\033) p Fl 2134 3097 a(1) p Fp 2173 3083 a(\() p Fn(!) s(;) p 2308 3083 a(\017) p Fj 2345 3097 a(F) p Fp 2404 3083 a(\)) p Fo(,) p Fn 2505 3083 a(\033) p Fl 2557 3097 a(2) p Fp 2596 3083 a(\() p Fn(!) s(;) p 2731 3083 a(\017) p Fj 2768 3097 a(F) p Fp 2827 3083 a(\)) p Fo 2899 3083 a(may) p 3100 3083 a(b) p 3137 3083 a(e) p 3215 3083 a(inter-) 448 3207 y(change) p 712 3207 a(d.) p 833 3207 a(However,) p 1233 3207 a(in) p 1345 3207 a(The) p 1493 3207 a(or) p 1572 3207 a(em) p 1724 3207 a(1,) p 1832 3207 a(the) p 1984 3207 a(exchange) p 2371 3207 a(of) p 2479 3207 a(two) p 2650 3207 a(op) p 2737 3207 a(er) p 2812 3207 a(ations,) p Fp 3115 3207 a(lim) p Fm 3241 3222 a(E) p 3284 3222 a(#) p Fl(0) 3388 3172 y(1) p 3384 3187 43 4 v Fm 3384 3239 a(E) p Fo 448 3332 a(and) p Fi 625 3263 a(R) p Fm 681 3289 a(1) p Fl 665 3359 a(0) p Fn 771 3332 a(dt) p 866 3332 a(\016) s(e) p Fm 951 3299 a(\000) p Fj(\016) r(t) p Fo 1103 3332 a(is) p 1202 3332 a(al) p 1276 3332 a(lowe) p 1442 3332 a(d) p 1523 3332 a(\(R) p 1621 3332 a(emark) p 1897 3332 a(4.1\)) p 2088 3332 a(if,) p 2205 3332 a(in) p 2317 3332 a(addition,) p 2701 3332 a(we) p 2837 3332 a(assume) p 3155 3332 a(the) p 3307 3332 a(fol-) 448 3456 y(lowing) p 732 3456 a(dynamic) p 1058 3456 a(al) p 1162 3456 a(lo) p 1226 3456 a(c) p 1263 3456 a(alization) p 1633 3456 a(estimate) p Fe 1065 3656 a(E) p Fh(j) p Fn(e) p Fm 1201 3618 a(\000) p Fj(itH) p Ff 1363 3626 a(!) p Fp 1412 3656 a(\() p Fn(!) p Fp 1523 3656 a(;) p Fn 1563 3656 a(x;) p 1655 3656 a(y) p Fp 1703 3656 a(\)) p Fh(j) p 1789 3656 a(\024) p Fn 1885 3656 a(C) p 1957 3656 a(e) p Fm 1999 3618 a(\000) p Fj(\026) p Fm(j) p Fj(x) p Fm(\000) p Fj(y) p Fm 2248 3618 a(j) p Fn 2271 3656 a(;) p 2405 3656 a(x;) p 2522 3656 a(y) p Fh 2595 3656 a(2) p Fk 2681 3656 a(Z) p 2700 3656 a(Z) p Fj 2755 3618 a(d) p Fn 2796 3656 a(;) p Fp 448 3656 a(\(1.8\)) 448 3856 y @beginspecial @setspecial @endspecial Fo(for) p 595 3856 a(some) p 829 3856 a(c) p 866 3856 a(onstants) p Fn 1230 3856 a(C) p 1329 3856 a(>) p Fp 1428 3856 a(0) p Fo(,) p Fn 1536 3856 a(\026) p 1619 3856 a(>) p Fp 1717 3856 a(0) p Fo(,) p 1825 3856 a(indep) p 2033 3856 a(endent) p 2331 3856 a(of) p Fn 2439 3856 a(t) p Fh 2500 3856 a(2) p Fp 2588 3856 a(I) p 2606 3856 a(R) p Fo(.) p 2747 3856 a(\(1.8\)) p 2976 3856 a(is) p 3076 3856 a(known) p 3360 3856 a(to) 448 3980 y(b) p 485 3980 a(e) p 560 3980 a(true) p 751 3980 a(when) p Fn 984 3980 a(\025) p 1062 3980 a(>) p Fp 1158 3980 a(0) p Fo 1236 3980 a(is) p 1334 3980 a(su\016ciently) p 1792 3980 a(lar) p 1894 3980 a(ge) p 2012 3980 a(\(high) p 2244 3980 a(disor) p 2434 3980 a(der) p 2595 3980 a(c) p 2632 3980 a(ase[2) q(,) p 2892 3980 a(4) q(]\).) 589 4105 y @beginspecial @setspecial @endspecial(\(3\)) p 748 4105 a(In) p 872 4105 a([12) q(],) p 1088 4105 a(essential) p 1429 4105 a(ly) p 1534 4105 a(the) p 1691 4105 a(same) p 1928 4105 a(r) p 1961 4105 a(esult) p 2181 4105 a(is) p 2284 4105 a(pr) p 2363 4105 a(ove) p 2488 4105 a(d) p 2574 4105 a(under) p 2838 4105 a(mor) p 2991 4105 a(e) p 3072 4105 a(r) p 3105 4105 a(estricte) p 3389 4105 a(d) 448 4229 y(situations) p 865 4229 a(\(i.e.,) p 1088 4229 a(b) p 1125 4229 a(ounde) p 1354 4229 a(d) p 1435 4229 a(r) p 1468 4229 a(andom) p 1766 4229 a(p) p 1807 4229 a(otential,) p 2166 4229 a(b) p 2203 4229 a(ounde) p 2432 4229 a(d) p 2513 4229 a(ele) p 2615 4229 a(ctric) p 2790 4229 a(al) p 2893 4229 a(p) p 2934 4229 a(otential,) p 3293 4229 a(and) 448 4354 y(high) p 648 4354 a(disor) p 838 4354 a(der\).) p 1087 4354 a(However,) p 1492 4354 a(ther) p 1643 4354 a(e) p 1723 4354 a(ar) p 1802 4354 a(e) p 1882 4354 a(some) p 2119 4354 a(di\013er) p 2324 4354 a(enc) p 2454 4354 a(es) p 2571 4354 a(b) p 2608 4354 a(etwe) p 2777 4354 a(en) p 2907 4354 a(the) p 3063 4354 a(de\014nition) 448 4478 y(of) p Fn 560 4478 a(\033) p Fl 612 4492 a(1) p Fp 652 4478 a(\() p Fn(!) s(;) p 787 4478 a(\017) p Fj 824 4492 a(F) p Fp 883 4478 a(\)) p Fo 956 4478 a(and) p 1137 4478 a(the) p 1293 4478 a(char) p 1460 4478 a(ge) p 1583 4478 a(tr) p 1646 4478 a(ansp) p 1821 4478 a(ort) p 1976 4478 a(de\014ne) p 2203 4478 a(d) p 2288 4478 a(in) p 2404 4478 a([12) q(].) p 2638 4478 a(F) p 2690 4478 a(or) p 2812 4478 a(instanc) p 3092 4478 a(e,) p 3202 4478 a(in) p 3319 4478 a(the) 448 4603 y(de\014nition) p 867 4603 a(of) p Fn 987 4603 a(\033) p Fl 1039 4617 a(1) p Fp 1078 4603 a(\() p Fn(!) s(;) p 1213 4603 a(\017) p Fj 1250 4617 a(F) p Fp 1309 4603 a(\)) p Fo(,) p 1420 4603 a(we) p 1568 4603 a(take) p Fh 1773 4603 a(E) p 1877 4603 a(#) p Fp 1970 4603 a(0) p Fo 2060 4603 a(limit) p 2289 4603 a(\014rst) p 2491 4603 a(and) p 2680 4603 a(then) p 2894 4603 a(take) p 3099 4603 a(the) p 3263 4603 a(time) 448 4727 y(aver) p 611 4727 a(age,) p 805 4727 a(while,) p 1069 4727 a(in) p 1182 4727 a([12) q(],) p 1394 4727 a(we) p 1531 4727 a(take) p 1726 4727 a(these) p 1959 4727 a(two) p 2131 4727 a(op) p 2218 4727 a(er) p 2293 4727 a(ations) p 2568 4727 a(at) p 2680 4727 a(the) p 2833 4727 a(same) p 3068 4727 a(time) p 3277 4727 a(in) p 3391 4727 a(a) 448 4852 y(sense.) p 727 4852 a(It) p 825 4852 a(would) p 1083 4852 a(not) p 1243 4852 a(b) p 1280 4852 a(e) p 1355 4852 a(e) p 1392 4852 a(asy) p 1552 4852 a(to) p 1662 4852 a(take) p 1855 4852 a(these) p 2085 4852 a(two) p 2254 4852 a(limits) p 2508 4852 a(at) p 2617 4852 a(the) p 2768 4852 a(same) p 3000 4852 a(time) p 3207 4852 a(in) p 3319 4852 a(the) 448 4976 y(appr) p 619 4976 a(o) p 660 4976 a(ach) p 830 4976 a(of) p 937 4976 a(this) p 1112 4976 a(p) p 1153 4976 a(ap) p 1240 4976 a(er.) p Fp 1920 5225 a(4) p eop %%Page: 5 5 5 4 bop 589 573 a @beginspecial @setspecial @endspecial Fo(\(4\)) p 755 573 a(In) p 886 573 a([8],) p 1064 573 a(they) p 1271 573 a(ar) p 1350 573 a(gue) p 1528 573 a(that) p 1726 573 a(the) p 1889 573 a(c) p 1926 573 a(onductivity) p 2408 573 a(is) p 2518 573 a(always) p 2820 573 a(zer) p 2932 573 a(o) p 3024 573 a(or) p 3154 573 a(in\014nity) 448 697 y(without) p 781 697 a(taking) p 1063 697 a(dissip) p 1280 697 a(ation) p 1526 697 a(me) p 1637 697 a(chanism) p 2006 697 a(into) p 2204 697 a(ac) p 2287 697 a(c) p 2324 697 a(ount.) p 2601 697 a(Mor) p 2762 697 a(e) p 2799 697 a(over,) p 3041 697 a(they) p 3247 697 a(show) 448 822 y(that) p 647 822 a(the) p 810 822 a(c) p 847 822 a(onductivity) p 1329 822 a(is) p 1440 822 a(always) p 1743 822 a(zer) p 1855 822 a(o) p 1947 822 a(if) p 2048 822 a(the) p 2211 822 a(Hamiltonian) p 2749 822 a(is) p 2859 822 a(b) p 2896 822 a(ounde) p 3125 822 a(d.) p 3280 822 a(Our) 448 946 y(r) p 481 946 a(esults) p 741 946 a(imply) p 998 946 a(that) p 1193 946 a(this) p 1375 946 a(is) p 1481 946 a(also) p 1676 946 a(true) p 1876 946 a(in) p 1996 946 a(c) p 2033 946 a(ase) p 2199 946 a(A) n(nderson) p 2618 946 a(lo) p 2682 946 a(c) p 2719 946 a(alization) p 3098 946 a(happ) p 3277 946 a(ens,) 448 1071 y(even) p 662 1071 a(when) p 898 1071 a(the) p 1054 1071 a(Hamiltonian) p 1583 1071 a(is) p 1685 1071 a(unb) p 1822 1071 a(ounde) p 2051 1071 a(d.) p 2181 1071 a(On) p 2339 1071 a(the) p 2494 1071 a(other) p 2734 1071 a(hand,) p 2991 1071 a(in) p 3106 1071 a([2) q(],) p 3274 1071 a(they) 448 1196 y(discuss) p 760 1196 a(the) p 914 1196 a(derivation) p 1348 1196 a(of) p 1458 1196 a(Kub) p 1614 1196 a(o) p 1696 1196 a(formula,) p 2065 1196 a(and) p 2245 1196 a(obtaine) p 2525 1196 a(d) p 2608 1196 a(the) p 2762 1196 a(same) p 2997 1196 a(quantity) p 3353 1196 a(as) 448 1320 y(what) p 664 1320 a(we) p 799 1320 a(wil) p 915 1320 a(l) p 971 1320 a(have) p 1180 1320 a(in) p 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Fn(x) p Fp(\)) p Fn(;) p 2731 2198 a(') p Fh 2815 2198 a(2) p Fn 2901 2198 a(l) p Fl 2930 2161 a(2) p Fp 2970 2198 a(\() p Fk(Z) p 3025 2198 a(Z) p Fl 3080 2161 a(2) p Fp 3119 2198 a(\)) p Fn(;) 448 2474 y @beginspecial @setspecial @endspecial Fp(where,) p Fn 801 2720 a(h) p Fj 853 2734 a(B) p Fp 914 2720 a(\() p Fn(x;) p 1041 2720 a(y) p Fp 1089 2720 a(\)) p 1150 2720 a(:=) p Fi 1271 2576 a(\() p Fn 1353 2680 a(e) p Ff 1405 2617 a(iB) p 1405 2629 71 4 v Fc 1426 2670 a(2) p Fj 1486 2644 a() p Fc 1797 2668 a(I) p 1808 2668 a(R) 1852 2653 y(2) p Fn 1895 2680 a(;) p Fp 2011 2680 a(if) p Fh 2094 2680 a(j) p Fn(x) p Fh 2192 2680 a(\000) p Fn 2283 2680 a(y) p Fh 2331 2680 a(j) p Fp 2381 2680 a(=) p 2477 2680 a(1,) 1353 2793 y(0) p Fn(;) p Fp 2011 2793 a(otherwise,) p Fn 2694 2720 a(x;) p 2786 2720 a(y) p Fh 2859 2720 a(2) p Fk 2945 2720 a(Z) p 2965 2720 a(Z) p Fl 3020 2682 a(2) p Fn 3059 2720 a(:) 448 2984 y(<) p Fh 561 2984 a(\001) p Fn(;) p Fh 626 2984 a(\001) p Fn 695 2984 a(>) p Fl 766 3012 a(I) p 779 3012 a(R) p Ff 831 2987 a(d) p Fp 912 2984 a(is) p 1014 2984 a(the) p 1181 2984 a(inner) p 1424 2984 a(pro) s(duct) p 1775 2984 a(on) p 1912 2984 a(I) p 1930 2984 a(R) p Fj 1996 2948 a(d) p Fp 2037 2984 a(.) p 2133 2984 a(W) p 2218 2984 a(e) p 2300 2984 a(de\014ne) p 2573 2984 a(the) p 2740 2984 a(Hall) p 2945 2984 a(conductivit) m(y) p Fn 448 3108 a(\033) p Fj 503 3075 a(H) p Fl 500 3131 a(1) p Fp 571 3108 a(\() p Fn(!) s(;) p 706 3108 a(\017) p Fj 743 3122 a(F) p Fp 802 3108 a(\),) p Fn 899 3108 a(\033) p Fj 954 3075 a(H) p Fl 951 3131 a(2) p Fp 1022 3108 a(\() p Fn(!) s(;) p 1157 3108 a(\017) p Fj 1194 3122 a(F) p Fp 1253 3108 a(\),) p 1351 3108 a(b) m(y) p 1482 3108 a(replacing) p Fn 1877 3108 a(x) p Fl 1929 3122 a(1) p Fp 2004 3108 a(b) m(y) p Fn 2135 3108 a(x) p Fl 2187 3122 a(2) p Fp 2262 3108 a(in) p 2374 3108 a(the) p 2536 3108 a(de\014nition) p 2945 3108 a(of) p Fn 3054 3108 a(\033) p Fl 3106 3122 a(1) p Fp 3145 3108 a(\() p Fn(!) s(;) p 3280 3108 a(\017) p Fj 3317 3122 a(F) p Fp 3377 3108 a(\),) p Fn 448 3233 a(\033) p Fl 500 3247 a(2) p Fp 540 3233 a(\() p Fn(!) s(;) p 675 3233 a(\017) p Fj 712 3247 a(F) p Fp 771 3233 a(\),) p 857 3233 a(resp) s(ectiv) m(ely) p 1315 3233 a(.) p 1378 3233 a(W) p 1463 3233 a(e) p 1528 3233 a(note) p 1724 3233 a(that) p 1914 3233 a(dissipation) p 2363 3233 a(mec) m(hanism) p 2824 3233 a(is) p 2909 3233 a(not) p 3065 3233 a(necessary) 448 3357 y(to) p 568 3357 a(consider) p 931 3357 a(in) p 1046 3357 a(the) p 1211 3357 a(de\014nition) p 1623 3357 a(of) p 1735 3357 a(the) p 1901 3357 a(Hall) p 2104 3357 a(conductivit) m(y) p 2589 3357 a(.) p 2680 3357 a(Under) p 2964 3357 a(Assumption) 448 3482 y(\(1.6\),) p 698 3482 a(w) m(e) p 838 3482 a(ha) m(v) m(e) p 1053 3482 a(the) p 1215 3482 a(follo) m(wing) p 1605 3482 a(result) p 1864 3482 a(whic) m(h) p 2130 3482 a(can) p 2303 3482 a(b) s(e) p 2432 3482 a(pro) m(v) m(ed) p 2734 3482 a(b) m(y) p 2866 3482 a(mimic) m(king) p 3311 3482 a(the) 448 3606 y(pro) s(of) p 686 3606 a(of) p 789 3606 a(Theorem) p 1174 3606 a(1,) p 1275 3606 a(2.) 448 3856 y @beginspecial @setspecial @endspecial Fe(Theorem) p 892 3856 a(3) p Fp 448 3980 a(\(1\)) p Fn 595 3980 a(\033) p Fl 647 3994 a(1) p Fp 686 3980 a(\() p Fn(!) s(;) p 821 3980 a(\017) p Fj 858 3994 a(F) p Fp 917 3980 a(\)) p 978 3980 a(=) p Fn 1074 3980 a(\033) p Fl 1126 3994 a(2) p Fp 1165 3980 a(\() p Fn(!) s(;) p 1300 3980 a(\017) p Fj 1337 3994 a(F) p Fp 1396 3980 a(\)) p 1457 3980 a(=) p 1553 3980 a(0) p Fn(;) p 1730 3980 a(a:e:) p 1896 3980 a(!) p Fp 1956 3980 a(.) 448 4105 y(\(2\)) p Fn 595 4105 a(\033) p Fj 650 4072 a(H) p Fl 647 4128 a(1) p Fp 717 4105 a(\() p Fn(!) s(;) p 852 4105 a(\017) p Fj 889 4119 a(F) p Fp 948 4105 a(\)) p 1009 4105 a(=) p Fn 1105 4105 a(\033) p Fj 1160 4072 a(H) p Fl 1157 4128 a(2) p Fp 1227 4105 a(\() p Fn(!) s(;) p 1362 4105 a(\017) p Fj 1399 4119 a(F) p Fp 1458 4105 a(\)) p 1519 4105 a(=) p Fn 1615 4105 a(i) p Fh(T) p Fp 1719 4105 a(\() p Fn(P) p Fj 1812 4119 a(\017) p 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p Fp 1424 4478 a([) p Fn(@) p Fl 1497 4492 a(1) p Fn 1537 4478 a(P) p Fj 1595 4492 a(\017) p Ff 1624 4503 a(F) p Fn 1678 4478 a(;) p 1718 4478 a(@) p Fl 1766 4492 a(2) p Fn 1807 4478 a(P) p Fj 1865 4492 a(\017) p Ff 1894 4503 a(F) p Fp 1948 4478 a(]) p Fn(P) p Fj 2031 4492 a(\017) p Ff 2060 4503 a(F) p Fp 2116 4478 a(\)) p 2182 4478 a(is) p 2275 4478 a(kno) m(wn) p 2564 4478 a(to) p 2677 4478 a(ha) m(v) m(e) p 2887 4478 a(an) p 3015 4478 a(in) m(terpreta-) 448 4603 y(tion) p 638 4603 a(as) p 753 4603 a(a) p 832 4603 a(\\top) s(ological) p 1342 4603 a(in) m(v) p 1459 4603 a(arian) m(t") p 1772 4603 a(\([6) r(,) p 1937 4603 a(8) q(]) p 2041 4603 a(and) p 2221 4603 a(references) p 2642 4603 a(therein\).) p 3030 4603 a(Therefore,) 448 4727 y(Theorem) p 831 4727 a(3) p 905 4727 a(implies) p 1213 4727 a(the) p 1368 4727 a(v) p 1411 4727 a(anishmen) m(t) p 1847 4727 a(of) p 1949 4727 a(the) p 2104 4727 a(direct) p 2360 4727 a(conductivit) m(y) p 2882 4727 a(and) p 3057 4727 a(the) p 3212 4727 a(quan-) 448 4852 y(tization) p 792 4852 a(of) p 907 4852 a(the) p 1074 4852 a(Hall) p 1279 4852 a(conductivit) m(y) p 1812 4852 a(if) p 1906 4852 a(the) p 2073 4852 a(F) p 2124 4852 a(ermi) p 2343 4852 a(energy) p 2645 4852 a(lies) p 2812 4852 a(in) p 2929 4852 a(the) p 3096 4852 a(lo) s(calized) 448 4976 y(regime,) p 767 4976 a(whic) m(h) p 1027 4976 a(is) p 1118 4976 a(w) m(ell-kno) m(wn) p 1590 4976 a(in) p 1697 4976 a(the) p 1853 4976 a(theory) p 2139 4976 a(of) p 2242 4976 a(in) m(tegral) p 2573 4976 a(quan) m(tum) p 2957 4976 a(Hall) p 3152 4976 a(e\013ect.) 1920 5225 y(5) p eop %%Page: 6 6 6 5 bop 589 573 a @beginspecial @setspecial @endspecial Fp(The) p 775 573 a(k) m(ey) p 938 573 a(ingredien) m(t) p 1363 573 a(of) p 1466 573 a(the) p 1621 573 a(pro) s(of) p 1857 573 a(of) p 1959 573 a(Theorem) p 2342 573 a(1,) p 2442 573 a(2) p 2516 573 a(is) p 2606 573 a(the) p 2761 573 a(theory) p 3046 573 a(dev) m(elop) s(ed) 448 697 y(in) p 555 697 a([2) q(,) p 682 697 a(8],) p 809 697 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1386 1445 a(In) p 1507 1445 a(order) p 1753 1445 a(for) p 1899 1445 a(that,) p 2131 1445 a(w) m(e) p 2272 1445 a(pro) m(v) m(e) p 2525 1445 a(resolv) m(en) m(t) p 2914 1445 a(equation) p 3293 1445 a(\(for) 448 1569 y(Theorem) p 832 1569 a(1\),) p 969 1569 a(and) p 1146 1569 a(Duhamel) p 1533 1569 a(form) m(ula) p 1867 1569 a(\(for) p 2041 1569 a(Theorem) p 2425 1569 a(2\),) p 2562 1569 a(resp) s(ectiv) m(ely) p 3020 1569 a(.) p Fq 448 1854 a(2) p 650 1854 a(Preliminaries) 448 2069 y @beginspecial @setspecial @endspecial Fp(In) p 560 2069 a(this) p 736 2069 a(section,) p 1063 2069 a(w) m(e) p 1195 2069 a(de\014ne) p 1456 2069 a(a) p 1530 2069 a(Hilb) s(ert) p 1842 2069 a(space) p Fh 2083 2069 a(L) p Fl 2146 2036 a(2) p Fp 2185 2069 a(,) p 2239 2069 a(study) p 2488 2069 a(its) p 2613 2069 a(basic) p 2839 2069 a(prop) s(erties,) p 3291 2069 a(and) 448 2193 y(consider) p 803 2193 a(some) p 1031 2193 a(op) s(erators) p 1433 2193 a(on) p 1560 2193 a(it.) p 1686 2193 a(First) p 1908 2193 a(of) p 2012 2193 a(all,) p 2163 2193 a(w) m(e) p 2297 2193 a(notice) p 2565 2193 a(that,) p 2788 2193 a(the) p 2944 2193 a(op) s(erator) p Fn 3311 2193 a(H) p Fj 3387 2207 a(!) p Fp 448 2318 a(is) p 540 2318 a(co) m(v) p 665 2318 a(arian) m(t) p 931 2318 a(w.r.t.) p 1184 2318 a(the) p 1341 2318 a(translation) p 1801 2318 a(in) p 1907 2318 a(the) p 2064 2318 a(follo) m(wing) p 2448 2318 a(sense) p Fn 1135 2525 a(U) p Fp 1207 2525 a(\() p Fn(a) p Fp(\)) p Fn(H) p Fj 1401 2539 a(!) p Fn 1451 2525 a(U) p Fp 1523 2525 a(\() p Fn(a) p Fp(\)) p Fm 1641 2488 a(\003) p Fp 1707 2525 a(=) p Fn 1803 2525 a(H) p Fj 1879 2539 a(T) p Ff 1930 2520 a(a) p Fj 1967 2539 a(!) p Fn 2017 2525 a(;) p 2149 2525 a(a) p Fh 2222 2525 a(2) p Fk 2308 2525 a(Z) p 2328 2525 a(Z) p Fj 2383 2488 a(d) p Fn 2423 2525 a(;) p 2489 2525 a(!) p Fh 2574 2525 a(2) p Fp 2660 2525 a(\012) p Fn(;) p Fp 448 2525 a(\(2.1\)) 448 2732 y @beginspecial @setspecial @endspecial(where) p Fn 723 2732 a(U) p Fp 795 2732 a(\() p Fn(a) p Fp(\)) p 956 2732 a(is) p 1060 2732 a(the) p 1228 2732 a(translation) p 1701 2732 a(op) s(erator) p 2079 2732 a(on) p Fn 2217 2732 a(l) p Fl 2246 2699 a(2) p Fp 2286 2732 a(\() p Fk(Z) p 2341 2732 a(Z) p Fj 2396 2696 a(d) p Fp 2436 2732 a(\):) p 2561 2732 a(\() p Fn(U) p Fp 2668 2732 a(\() p Fn(a) p Fp(\)) p Fn(') p Fp(\)\() p Fn(x) p Fp(\)) p 3050 2732 a(:=) p Fn 3191 2732 a(') p Fp(\() p Fn(x) p Fh 3366 2732 a(\000) p Fn 448 2857 a(a) p Fp(\),) p Fn 598 2857 a(U) p Fp 670 2857 a(\() p Fn(a) p Fp(\)) p Fm 788 2824 a(\003) p Fp 867 2857 a(is) p 967 2857 a(the) p 1132 2857 a(adjoin) m(t) p 1448 2857 a(op) s(erator) p 1824 2857 a(of) p Fn 1936 2857 a(U) p Fp 2008 2857 a(\() p Fn(a) p Fp(\),) p 2192 2857 a(and) p Fn 2378 2857 a(T) p Fj 2444 2824 a(a) p Fp 2525 2857 a(:) p 2589 2857 a(\012) p Fh 2694 2857 a(!) p Fp 2825 2857 a(\012) p 2929 2857 a(is) p 3029 2857 a(a) p 3113 2857 a(measure) 448 2982 y(preserving) p 887 2982 a(map) p 1089 2982 a(de\014ned) p 1403 2982 a(b) m(y) p Fn 1530 2982 a(!) p Fp 1616 2982 a(=) p Fh 1713 2982 a(f) p Fn(V) p Fj 1811 2996 a(!) p Fp 1862 2982 a(\() p Fn(x) p Fp(\)) p Fh(g) p Fj 2029 3010 a(x) p Fm(2) p Fg(Z) p 2132 3010 a(Z) p Ff 2176 2985 a(d) p Fh 2242 2982 a(7!) p Fn 2359 2982 a(T) p Fj 2425 2949 a(a) p Fn 2467 2982 a(!) p Fp 2553 2982 a(=) p Fh 2650 2982 a(f) p Fn(V) p Fj 2748 2996 a(!) p Fp 2799 2982 a(\() p Fn(x) p Fh 2907 2982 a(\000) p Fn 2998 2982 a(a) p Fp(\)) p Fh(g) p Fj 3126 3010 a(x) p Fm(2) p Fg(Z) p 3229 3010 a(Z) p Ff 3272 2985 a(d) p Fn 3313 2982 a(:) p Fp 3369 2982 a(It) 448 3106 y(is) p 546 3106 a(w) m(ell-kno) m(wn) p 1025 3106 a(that) p Fn 1228 3106 a(T) p Fj 1294 3073 a(a) p Fp 1373 3106 a(is) p 1471 3106 a(ergo) s(dic.) p 1841 3106 a(Because) p 2196 3106 a(of) p 2306 3106 a(\(2.1\),) p 2556 3106 a(the) p 2719 3106 a(matrix) p 3022 3106 a(elemen) m(t) p 3364 3106 a(of) p Fn 448 3231 a(H) p Fj 524 3245 a(!) p Fp 605 3231 a(satis\014es) p 939 3231 a(the) p 1096 3231 a(follo) m(wing) p 1480 3231 a(relation) p Fn 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2210 3645 a(Z) p Fj 2265 3608 a(d) p Fh 2330 3645 a(\002) p Fk 2426 3645 a(Z) p 2446 3645 a(Z) p Fj 2500 3608 a(d) p Fp 2578 3645 a(satis\014es) p 2920 3645 a(\(CR\)) p 3160 3645 a(if) p 3250 3645 a(\(2.2\)) 448 3770 y(holds.) p 720 3770 a(W) p 805 3770 a(e) p 872 3770 a(de\014ne) p Fh 1131 3770 a(L) p Fl 1194 3737 a(2) p Fp 1259 3770 a(as) p 1366 3770 a(the) p 1519 3770 a(space) p 1757 3770 a(of) p 1857 3770 a(functions) p 2244 3770 a(on) p 2366 3770 a(\012) p Fh 2444 3770 a(\002) p Fk 2527 3770 a(Z) p 2547 3770 a(Z) p Fj 2601 3733 a(d) p Fh 2653 3770 a(\002) p Fk 2736 3770 a(Z) p 2756 3770 a(Z) p Fj 2810 3733 a(d) p Fp 2877 3770 a(whic) m(h) p 3133 3770 a(satis\014es) 448 3894 y(\(CR\)) p 682 3894 a(and) p 859 3894 a(has) p 1021 3894 a(a) p 1097 3894 a(certain) p 1400 3894 a(deca) m(ying) p 1774 3894 a(prop) s(ert) m(y) p 2108 3894 a(.) p Fh 660 4102 a(L) p Fl 723 4064 a(2) p Fp 787 4102 a(:=) p Fh 908 4102 a(f) p Fn(A) p Fp 1022 4102 a(\() p Fn(!) p Fp 1132 4102 a(;) p Fn 1172 4102 a(x;) p 1264 4102 a(y) p Fp 1312 4102 a(\)) p 1374 4102 a(:) p 1449 4102 a(function) p 1805 4102 a(on) p 1932 4102 a(\012) p Fh 2017 4102 a(\002) p Fk 2108 4102 a(Z) p 2128 4102 a(Z) p Fj 2183 4064 a(d) p Fh 2244 4102 a(\002) p Fk 2335 4102 a(Z) p 2355 4102 a(Z) p Fj 2409 4064 a(d) p Fp 2480 4102 a(whic) m(h) p 2740 4102 a(is) p 2832 4102 a(\014nite) p 3064 4102 a(a.e.,) 1127 4251 y(\(1\)) p Fn 1363 4251 a(A) p Fp(\() p Fn(!) p Fp 1542 4251 a(;) p Fn 1582 4251 a(x;) p 1674 4251 a(y) p Fp 1722 4251 a(\)) p 1788 4251 a(satis\014es) p 2123 4251 a(\(CR\),) 1127 4422 y(\(2\)) p Fh 1363 4422 a(k) p Fn(A) p Fh(k) p Fl 1521 4384 a(2) p Fm 1521 4449 a(L) p Fc 1570 4430 a(2) p Fp 1635 4422 a(:=) p Fi 1756 4307 a(Z) p Fl 1802 4496 a(\012) p Fn 1873 4422 a(d) p Fe(P) p Fi 2038 4341 a(X) p Fj 2007 4540 a(x) p Fm(2) p Fg(Z) p 2110 4540 a(Z) p Ff 2152 4514 a(d) p Fh 2204 4422 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2407 4422 a(;) p Fn 2447 4422 a(x;) p Fp 2539 4422 a(0\)) p Fh(j) p Fl 2644 4384 a(2) p Fn 2711 4422 a(<) p Fh 2807 4422 a(1g) p Fn(:) p Fe 448 4727 a(Remark) p 846 4727 a(2.1) p 1025 4727 a @beginspecial @setspecial @endspecial Fo(In) p 1139 4727 a(the) p 1285 4727 a(ab) p 1368 4727 a(ove) p 1527 4727 a(de\014nition,) p 1957 4727 a(\\a.e.") p 2223 4727 a(is) p 2316 4727 a(in) p 2423 4727 a(the) p 2569 4727 a(sense) p 2806 4727 a(of) p Fp 2921 4704 a(~) p Fe 2908 4727 a(P) p Fo 2980 4727 a(-a.e.,) p 3213 4727 a(wher) p 3394 4727 a(e) p Fp 461 4829 a(~) p Fe 448 4852 a(P) p Fo 550 4852 a(is) p 645 4852 a(the) p 793 4852 a(pr) p 872 4852 a(o) p 913 4852 a(duct) p 1112 4852 a(me) p 1223 4852 a(asur) p 1388 4852 a(e) p 1462 4852 a(of) p Fe 1566 4852 a(P) p Fo 1667 4852 a(and) p 1841 4852 a(the) p 1989 4852 a(c) p 2026 4852 a(ounting) p 2354 4852 a(me) p 2465 4852 a(asur) p 2630 4852 a(e) p 2703 4852 a(on) p Fk 2831 4852 a(Z) p 2850 4852 a(Z) p Fj 2905 4815 a(d) p Fh 2960 4852 a(\002) p Fk 3045 4852 a(Z) p 3064 4852 a(Z) p Fj 3119 4815 a(d) p Fo 3159 4852 a(.) p 3228 4852 a(Sinc) p 3395 4852 a(e) p Fk 448 4976 a(Z) p 467 4976 a(Z) p Fj 522 4939 a(d) p Fh 587 4976 a(\002) p Fk 681 4976 a(Z) p 700 4976 a(Z) p Fj 755 4939 a(d) p Fo 833 4976 a(is) p 936 4976 a(c) p 973 4976 a(ountable,) p 1370 4976 a(\\) p Fn(A) p Fp(\() p Fn(!) p Fp 1595 4976 a(;) p Fn 1635 4976 a(x;) p 1727 4976 a(y) p Fp 1775 4976 a(\)) p Fo 1849 4976 a(is) p 1951 4976 a(\014nite) p 2191 4976 a(for) p Fp 2354 4953 a(~) p Fe 2341 4976 a(P) p Fo 2413 4976 a(-a.e.") p 2674 4976 a(is) p 2776 4976 a(e) p 2813 4976 a(quivalent) p 3204 4976 a(to) p 3319 4976 a(the) p Fp 1920 5225 a(6) p eop %%Page: 7 7 7 6 bop Fo 448 573 a(statement) p 873 573 a(that) p 1068 573 a(\\ther) p 1266 573 a(e) p 1351 573 a(exists) p 1609 573 a(a) p 1697 573 a(subset) p Fp 1976 573 a(\012) p Fl 2042 587 a(0) p Fh 2123 573 a(\032) p Fp 2235 573 a(\012) p Fo 2342 573 a(with) p Fe 2549 573 a(P) p Fp(\(\012) p Fl 2721 587 a(0) p Fp 2761 573 a(\)) p 2838 573 a(=) p 2951 573 a(1) p Fo(,) p 3068 573 a(such) p 3284 573 a(that) p Fn 448 697 a(A) p Fp(\() p Fn(!) p Fp 627 697 a(;) p Fn 667 697 a(x;) p 759 697 a(y) p Fp 807 697 a(\)) p Fo 875 697 a(is) p 973 697 a(\014nite) p 1208 697 a(for) p Fn 1353 697 a(!) p Fh 1438 697 a(2) p Fp 1524 697 a(\012) p Fl 1590 711 a(0) p Fo 1629 697 a(,) p Fn 1689 697 a(x) p Fo(,) p Fn 1802 697 a(y) p Fh 1875 697 a(2) p Fk 1961 697 a(Z) p 1980 697 a(Z) p Fj 2034 661 a(d) p Fo 2075 697 a(".) 448 897 y @beginspecial @setspecial @endspecial Fp(W) p 533 897 a(e) p 600 897 a(shall) p 808 897 a(see) p 950 897 a(there) p 1178 897 a(are) p 1325 897 a(man) m(y) p 1568 897 a(functions) p 1956 897 a(whic) m(h) p 2211 897 a(b) s(elong) p 2497 897 a(to) p Fh 2603 897 a(L) p Fl 2666 864 a(2) p Fp 2705 897 a(.) p 2769 897 a(F) p 2820 897 a(or) p 2928 897 a(this) p 3100 897 a(purp) s(ose,) 448 1021 y(w) m(e) p 582 1021 a(consider) p 936 1021 a(a) p 1012 1021 a(subspace) p 1392 1021 a(of) p Fh 1496 1021 a(L) p Fl 1559 988 a(2) p Fp 1598 1021 a(.) p Fh 720 1237 a(A) p Fp 818 1237 a(:=) p Fh 939 1237 a(ff) p Fn(A) p Fj 1097 1251 a(!) p Fh 1148 1237 a(g) p Fj 1193 1251 a(!) p Fm 1239 1251 a(2) p Fl(\012) p Fp 1393 1237 a(:) p 1534 1237 a(family) p 1812 1237 a(of) p 1915 1237 a(b) s(ounded) p 2287 1237 a(op) s(erators) p 2689 1237 a(on) p Fn 2815 1237 a(l) p Fl 2844 1199 a(2) p Fp 2884 1237 a(\() p Fk(Z) p 2939 1237 a(Z) p Fj 2994 1199 a(d) p Fp 3034 1237 a(\)) p Fn(;) p Fp 1418 1386 a(\(1\)) p Fn 1549 1386 a(U) p Fp 1621 1386 a(\() p Fn(a) p Fp(\)) p Fn(A) p Fj 1807 1400 a(!) p Fn 1859 1386 a(U) p Fp 1931 1386 a(\() p Fn(a) p Fp(\)) p Fm 2049 1349 a(\003) p Fp 2114 1386 a(=) p Fn 2210 1386 a(A) p Fj 2278 1400 a(T) p Ff 2329 1382 a(a) p Fj 2367 1400 a(!) p Fn 2417 1386 a(;) p 2549 1386 a(!) p Fh 2634 1386 a(2) p Fp 2720 1386 a(\012) p Fn(;) p 2851 1386 a(a) p Fh 2924 1386 a(2) p Fk 3010 1386 a(Z) p 3030 1386 a(Z) p Fj 3085 1349 a(d) p Fn 3125 1386 a(;) p Fp 1418 1536 a(\(2\)) p 1553 1536 a(sup) p Fj 1549 1613 a(!) p Fm 1595 1613 a(2) p Fl(\012) p Fh 1709 1536 a(k) p Fn(A) p Fj 1822 1550 a(!) p Fh 1873 1536 a(k) p Fj 1918 1550 a(op) p Fn 2017 1536 a(<) p Fh 2113 1536 a(1g) p Fn(:) p Fh 448 1808 a(k) p Fn(A) p Fh(k) p Fj 606 1822 a(op) p Fp 711 1808 a(is) p 803 1808 a(the) p 959 1808 a(op) s(erator) p 1326 1808 a(norm) p 1564 1808 a(on) p Fn 1690 1808 a(l) p Fl 1719 1775 a(2) p Fp 1758 1808 a(\() p Fk(Z) p 1813 1808 a(Z) p Fj 1868 1771 a(d) p Fp 1909 1808 a(\).) p Fe 448 2007 a(Remark) p 846 2007 a(2.2) p 1025 2007 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1123 2007 a(A) p Fj 1191 2021 a(!) p Fh 1271 2007 a(2) p 1362 2007 a(A) p Fo(,) p 1498 2007 a(then) p 1703 2007 a(its) p 1833 2007 a(matrix) p 2128 2007 a(element) p Fn 2467 2007 a(A) p Fp(\() p Fn(!) p Fp 2630 2007 a(;) p Fn 2670 2007 a(x;) p 2762 2007 a(y) p Fp 2810 2007 a(\)) p Fo 2881 2007 a(b) p 2918 2007 a(elongs) p 3195 2007 a(to) p Fh 3307 2007 a(L) p Fl 3370 1974 a(2) p Fo 3409 2007 a(.) 448 2132 y(In) p 561 2132 a(fact,) p 763 2132 a(sinc) p 916 2132 a(e) p Fn 984 2132 a(A) p Fj 1052 2146 a(!) p Fo 1129 2132 a(is) p 1220 2132 a(b) p 1257 2132 a(ounde) p 1486 2132 a(d) p 1560 2132 a(on) p Fn 1684 2132 a(l) p Fl 1713 2099 a(2) p Fp 1752 2132 a(\() p Fk(Z) p 1806 2132 a(Z) p Fj 1861 2095 a(d) p Fp 1902 2132 a(\)) p Fo(,) p Fn 1993 2132 a(A) p Fp(\() p Fn(!) p Fp 2171 2132 a(;) p Fn 2211 2132 a(x;) p 2303 2132 a(y) p Fp 2351 2132 a(\)) p Fo 2413 2132 a(is) p 2505 2132 a(\014nite) p 2733 2132 a(for) p 2872 2132 a(any) p Fp 3040 2132 a(\() p Fn(!) s(;) p 3175 2132 a(x;) p 3267 2132 a(y) p Fp 3315 2132 a(\)) p Fh 3377 2132 a(2) p Fp 448 2256 a(\012) p Fh 522 2256 a(\002) p Fk 601 2256 a(Z) p 620 2256 a(Z) p Fj 675 2219 a(d) p Fh 723 2256 a(\002) p Fk 802 2256 a(Z) p 821 2256 a(Z) p Fj 876 2219 a(d) p Fo 916 2256 a(.) p 984 2256 a(The) p 1164 2256 a(c) p 1201 2256 a(ondition) p 1556 2256 a(\(1\)) p 1704 2256 a(in) p 1810 2256 a(the) p 1955 2256 a(de\014nition) p 2356 2256 a(of) p Fh 2457 2256 a(A) p Fo 2557 2256 a(implies) p 2862 2256 a(that) p Fn 3043 2256 a(A) p Fp(\() p Fn(!) p Fp 3221 2256 a(;) p Fn 3261 2256 a(x;) p 3353 2256 a(y) p Fp 3401 2256 a(\)) p Fo 448 2381 a(satis\014es) p 792 2381 a(\(CR\).) p 1060 2381 a(T) p 1118 2381 a(o) p 1200 2381 a(che) p 1325 2381 a(ck) p 1443 2381 a(the) p 1597 2381 a(c) p 1634 2381 a(ondition) p 1996 2381 a(\(2\)) p 2152 2381 a(in) p 2265 2381 a(the) p 2418 2381 a(de\014nition) p 2827 2381 a(of) p Fh 2936 2381 a(L) p Fl 2999 2348 a(2) p Fo 3038 2381 a(,) p 3102 2381 a(we) p 3238 2381 a(write) p Fn 448 2505 a(A) p Fp(\() p Fn(!) p Fp 627 2505 a(;) p Fn 667 2505 a(x;) p Fp 759 2505 a(0\)) p 866 2505 a(=) p 962 2505 a(\() p Fn(A) p Fj 1065 2519 a(!) p Fn 1116 2505 a(\016) p Fl 1156 2519 a(0) p Fp 1195 2505 a(\)\() p Fn(x) p Fp(\)) p Fo(,) p 1407 2505 a(and) p 1575 2505 a(sinc) p 1728 2505 a(e) p Fn 1794 2505 a(A) p Fj 1862 2519 a(!) p Fo 1937 2505 a(is) p 2026 2505 a(b) p 2063 2505 a(ounde) p 2292 2505 a(d) p 2364 2505 a(on) p Fn 2485 2505 a(l) p Fl 2514 2472 a(2) p Fp 2554 2505 a(\() p Fk(Z) p 2608 2505 a(Z) p Fj 2663 2468 a(d) p Fp 2703 2505 a(\)) p Fo(,) p 2792 2505 a(and) p Fh 2960 2505 a(k) p Fn(\016) p Fl 3045 2519 a(0) p Fh 3086 2505 a(k) p Fj 3131 2534 a(l) p Fc 3153 2515 a(2) p Fl 3188 2534 a(\() p Fg(Z) p 3230 2534 a(Z) p Ff 3273 2509 a(d) p Fl 3310 2534 a(\)) p Fp 3366 2505 a(=) 448 2642 y(1) p Fo 526 2642 a(\() p Fh(k) p 629 2642 a(\001) p 675 2642 a(k) p Fj 720 2671 a(l) p Fc 742 2652 a(2) p Fl 776 2671 a(\() p Fg(Z) p 818 2671 a(Z) p Ff 862 2645 a(d) p Fl 898 2671 a(\)) p Fo 963 2642 a(is) p Fn 1060 2642 a(l) p Fl 1089 2609 a(2) p Fp 1128 2642 a(\() p Fk(Z) p 1182 2642 a(Z) p Fj 1238 2605 a(d) p Fp 1278 2642 a(\)) p Fo(-norm\),) p Fi 1227 2795 a(X) p Fj 1196 2994 a(x) p Fm(2) p Fg(Z) p 1298 2994 a(Z) p Ff 1342 2968 a(d) p Fh 1393 2876 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 1597 2876 a(;) p Fn 1637 2876 a(x;) p Fp 1729 2876 a(0\)) p Fh(j) p Fl 1834 2839 a(2) p Fp 1900 2876 a(=) p Fh 1996 2876 a(k) p Fp(\() p Fn(A) p Fj 2144 2890 a(!) p Fn 2196 2876 a(\016) p Fl 2236 2890 a(0) p Fp 2275 2876 a(\)\() p Fn(x) p Fp(\)) p Fh(k) p Fl 2477 2839 a(2) p Fj 2477 2912 a(l) p Fc 2499 2893 a(2) p Fl 2535 2912 a(\() p Fg(Z) p 2577 2912 a(Z) p Ff 2621 2887 a(d) p Fl 2657 2912 a(\)) p Fh 1900 3120 a(\024) p 1996 3120 a(k) p Fn(A) p Fj 2109 3134 a(!) p Fh 2160 3120 a(k) p Fl 2205 3083 a(2) p Fj 2205 3143 a(op) p Fn 2279 3120 a(:) 448 3336 y @beginspecial @setspecial @endspecial Fo(The) p 633 3336 a(c) p 670 3336 a(ondition) p 1029 3336 a(\(2\)) p 1181 3336 a(in) p 1291 3336 a(the) p 1440 3336 a(de\014nition) p 1845 3336 a(of) p Fh 1951 3336 a(A) p Fo 2055 3336 a(now) p 2244 3336 a(implies) p Fh 2554 3336 a(k) p Fn(A) p Fh(k) p Fm 2712 3356 a(L) p Fc 2761 3337 a(2) p Fn 2825 3336 a(<) p Fh 2921 3336 a(1) p Fo(,) p 3071 3336 a(and) p 3247 3336 a(thus,) p Fn 448 3460 a(A) p Fp(\() p Fn(!) p Fp 627 3460 a(;) p Fn 667 3460 a(x;) p 759 3460 a(y) p Fp 807 3460 a(\)) p Fh 892 3460 a(2) p 1002 3460 a(L) p Fl 1065 3427 a(2) p Fo 1104 3460 a(.) p 1214 3460 a(Ther) p 1400 3460 a(efor) p 1549 3460 a(e,) p 1670 3460 a(we) p 1818 3460 a(wil) p 1934 3460 a(l) p 2003 3460 a(sometimes) p 2460 3460 a(abuse) p 2722 3460 a(the) p 2886 3460 a(notation,) p 3293 3460 a(and) 448 3585 y(r) p 481 3585 a(e) p 518 3585 a(gar) p 639 3585 a(d) p Fh 731 3585 a(A) p Fo 847 3585 a(as) p 974 3585 a(a) p 1064 3585 a(subsp) p 1270 3585 a(ac) p 1353 3585 a(e) p 1440 3585 a(of) p Fh 1558 3585 a(L) p Fl 1621 3552 a(2) p Fo 1660 3585 a(,) p 1734 3585 a(though) p 2038 3585 a(the) p 2200 3585 a(former) p 2510 3585 a(is) p 2619 3585 a(a) p 2709 3585 a(sp) p 2787 3585 a(ac) p 2870 3585 a(e) p 2957 3585 a(of) p 3075 3585 a(op) p 3162 3585 a(er) p 3237 3585 a(ators) 448 3709 y(while) p 681 3709 a(the) p 832 3709 a(latter) p 1074 3709 a(is) p 1172 3709 a(that) p 1358 3709 a(of) p 1465 3709 a(functions.) 448 3909 y @beginspecial @setspecial @endspecial Fp(T) p 506 3909 a(o) p 576 3909 a(in) m(tro) s(duce) p 975 3909 a(a) p 1045 3909 a(Hilb) s(ert) p 1352 3909 a(space) p 1589 3909 a(structure) p 1973 3909 a(on) p Fh 2093 3909 a(L) p Fl 2156 3876 a(2) p Fp 2196 3909 a(,) p 2246 3909 a(w) m(e) p 2374 3909 a(consider) 2744 3886 y(~) p Fh 2723 3909 a(L) p Fl 2786 3876 a(2) p Fp 2850 3909 a(:=) p Fn 2971 3909 a(L) p Fl 3033 3876 a(2) p Fp 3073 3909 a(\(\012) p Fh 3182 3909 a(\002) p Fk 3261 3909 a(Z) p 3281 3909 a(Z) p Fj 3336 3872 a(d) p Fp 3377 3909 a(\).) p Fe 448 4108 a(Prop) s(osition) p 1014 4108 a(2.1) p 1193 4108 a @beginspecial @setspecial @endspecial Fo(We) p 1358 4108 a(de\014ne) p 1623 4108 a(a) p 1702 4108 a(map) p Fn 1901 4108 a(\031) p Fp 1982 4108 a(:) p Fh 2032 4108 a(L) p Fl 2095 4075 a(2) p Fh 2160 4108 a(!) p Fp 2297 4085 a(~) p Fh 2276 4108 a(L) p Fl 2339 4075 a(2) p Fo 2410 4108 a(by) p Fp 1245 4324 a(\() p Fn(\031) s(A) p Fp(\)\() p Fn(!) s(;) p 1573 4324 a(x) p Fp(\)) p 1687 4324 a(:=) p Fn 1808 4324 a(A) p Fp(\() p Fn(!) p Fp 1987 4324 a(;) p Fn 2027 4324 a(x;) p Fp 2119 4324 a(0\)) p Fn(;) p 2334 4324 a(A) p Fh 2427 4324 a(2) p 2513 4324 a(L) p Fl 2576 4286 a(2) p Fn 2615 4324 a(:) 448 4540 y @beginspecial @setspecial @endspecial Fo(Then,) p Fn 713 4540 a(\031) p Fo 801 4540 a(is) p 898 4540 a(a) p 977 4540 a(bije) p 1112 4540 a(ction,) p 1370 4540 a(and) p Fp 1079 4756 a(\() p Fn(\031) p Fm 1169 4718 a(\000) p Fl(1) p Fn 1264 4756 a(a) p Fp(\)\() p Fn(!) p Fp 1457 4756 a(;) p Fn 1497 4756 a(x;) p 1589 4756 a(y) p Fp 1637 4756 a(\)) p 1699 4756 a(=) p Fn 1795 4756 a(a) p Fp(\() p Fn(T) p Fm 1944 4718 a(\000) p Fj(y) p Fn 2040 4756 a(!) s(;) p 2140 4756 a(x) p Fh 2213 4756 a(\000) p Fn 2303 4756 a(y) p Fp 2351 4756 a(\)) p Fn(;) p 2520 4756 a(a) p Fh 2593 4756 a(2) p Fp 2700 4733 a(~) p Fh 2679 4756 a(L) p Fl 2742 4718 a(2) p Fn 2781 4756 a(:) p Fp 1920 5225 a(7) p eop %%Page: 8 8 8 7 bop 448 573 a @beginspecial @setspecial @endspecial Fo(Pr) p 543 573 a(o) p 584 573 a(of.) p Fp 725 573 a(It) p 815 573 a(is) p 898 573 a(clear) p 1107 573 a(that) p Fn 1295 573 a(\031) s(A) p Fh 1443 573 a(2) p Fp 1550 550 a(~) p Fh 1529 573 a(L) p Fl 1592 540 a(2) p Fp 1653 573 a(for) p Fn 1783 573 a(A) p Fh 1877 573 a(2) p 1963 573 a(L) p Fl 2026 540 a(2) p Fp 2065 573 a(.) p 2128 573 a(Con) m(v) m(ersely) p 2550 573 a(,) p 2599 573 a(let) p 2721 573 a(\() p Fn(\031) p Fm 2811 540 a(\000) p Fl(1) p Fn 2906 573 a(a) p Fp(\)\() p Fn(!) p Fp 3100 573 a(;) p Fn 3140 573 a(x;) p 3232 573 a(y) p Fp 3280 573 a(\)) p 3341 573 a(:=) p Fn 448 697 a(a) p Fp(\() p Fn(T) p Fm 597 664 a(\000) p Fj(y) p Fn 694 697 a(!) s(;) p 794 697 a(x) p Fh 866 697 a(\000) p Fn 957 697 a(y) p Fp 1005 697 a(\),) p Fn 1096 697 a(a) p Fh 1169 697 a(2) p Fp 1276 674 a(~) p Fh 1255 697 a(L) p Fl 1318 664 a(2) p Fp 1357 697 a(.) p 1423 697 a(By) p 1565 697 a(Remark) p 1908 697 a(2.1,) p 2080 697 a(\() p Fn(\031) p Fm 2170 664 a(\000) p Fl(1) p Fn 2264 697 a(a) p Fp(\)\() p Fn(!) p Fp 2458 697 a(;) p Fn 2498 697 a(x;) p 2590 697 a(y) p Fp 2638 697 a(\)) p 2704 697 a(is) p 2796 697 a(\014nite) p 3028 697 a(a.e.) 693 913 y(\() p Fn(\031) p Fm 783 876 a(\000) p Fl(1) p Fn 878 913 a(a) p Fp(\)\() p Fn(T) p Fm 1062 876 a(\000) p Fj(b) p Fn 1151 913 a(!) p Fp 1226 913 a(;) p Fn 1266 913 a(x) p Fh 1339 913 a(\000) p Fn 1430 913 a(b;) p 1509 913 a(y) p Fh 1577 913 a(\000) p Fn 1668 913 a(b) p Fp(\)) p 1768 913 a(=) p Fn 1864 913 a(a) p Fp(\() p Fn(T) p Fm 2013 876 a(\000) p Fj(b) p Fn 2102 913 a(T) p Fm 2168 876 a(\000) p Fl(\() p Fj(y) p Fm 2287 876 a(\000) p Fj(b) p Fl(\)) p Fn 2404 913 a(!) s(;) p Fp 2504 913 a(\() p Fn(x) p Fh 2612 913 a(\000) p Fn 2703 913 a(b) p Fp(\)) p Fh 2798 913 a(\000) p Fp 2888 913 a(\() p Fn(y) p Fh 2992 913 a(\000) p Fn 3083 913 a(b) p Fp(\)\)) 1768 1063 y(=) p Fn 1864 1063 a(a) p Fp(\() p Fn(T) p Fm 2013 1025 a(\000) p Fj(y) p Fn 2109 1063 a(!) s(;) p 2209 1063 a(x) p Fh 2282 1063 a(\000) p Fn 2373 1063 a(y) p Fp 2421 1063 a(\)) 1768 1212 y(=) p 1864 1212 a(\() p Fn(\031) p Fm 1954 1175 a(\000) p Fl(1) p Fn 2049 1212 a(a) p Fp(\)\() p Fn(!) p Fp 2242 1212 a(;) p Fn 2282 1212 a(x;) p 2374 1212 a(y) p Fp 2422 1212 a(\)) p Fn(;) p 2590 1212 a(x;) p 2682 1212 a(y) s(;) p 2770 1212 a(b) p Fh 2835 1212 a(2) p Fk 2920 1212 a(Z) p 2940 1212 a(Z) p Fj 2995 1175 a(d) p Fn 3036 1212 a(:) 448 1428 y @beginspecial @setspecial @endspecial Fp(Hence) p 725 1428 a(\() p Fn(\031) p Fm 815 1395 a(\000) p Fl(1) p Fn 910 1428 a(a) p Fp(\)\() p Fn(!) p Fp 1104 1428 a(;) p Fn 1144 1428 a(x;) p 1236 1428 a(y) p Fp 1284 1428 a(\)) p 1357 1428 a(satis\014es) p 1698 1428 a(\(CR\).) p Fh 1964 1428 a(k) p Fn(\031) p Fm 2064 1395 a(\000) p Fl(1) p Fn 2159 1428 a(a) p Fh(k) p Fm 2252 1448 a(L) p Fc 2301 1429 a(2) p Fp 2376 1428 a(=) p Fh 2483 1428 a(k) p Fn(a) p Fh(k) p Fl 2639 1441 a(~) p Fm 2621 1458 a(L) p Fc 2670 1439 a(2) p Fn 2746 1428 a(<) p Fh 2853 1428 a(1) p Fp(.) p 3030 1428 a(Therefore,) p Fn 448 1553 a(\031) p Fm 503 1520 a(\000) p Fl(1) p Fn 598 1553 a(a) p Fh 694 1553 a(2) p 802 1553 a(L) p Fl 865 1520 a(2) p Fp 949 1553 a(for) p Fn 1101 1553 a(a) p Fh 1197 1553 a(2) p Fp 1327 1530 a(~) p Fh 1306 1553 a(L) p Fl 1369 1520 a(2) p Fp 1408 1553 a(.) p 1515 1553 a(Then,) p 1795 1553 a(it) p 1899 1553 a(su\016ces) p 2222 1553 a(to) p 2347 1553 a(sho) m(w) p Fn 2586 1553 a(\031) p Fm 2641 1520 a(\000) p Fl(1) p Fh 2764 1553 a(\016) p Fn 2839 1553 a(\031) p Fp 2938 1553 a(and) p Fn 3129 1553 a(\031) p Fh 3213 1553 a(\016) p Fn 3288 1553 a(\031) p Fm 3343 1520 a(\000) p Fl(1) p Fp 448 1677 a(are) p 601 1677 a(equal) p 842 1677 a(to) p 954 1677 a(iden) m(tities) p 1347 1677 a(on) p Fh 1474 1677 a(L) p Fl 1537 1644 a(2) p Fp 1607 1677 a(and) 1806 1654 y(~) p Fh 1785 1677 a(L) p Fl 1848 1644 a(2) p Fp 1919 1677 a(resp) s(ectiv) m(ely) p 2377 1677 a(,) p 2433 1677 a(whic) m(h) p 2694 1677 a(follo) m(ws) p 2994 1677 a(from) p 3210 1677 a(direct) 448 1802 y(computations.) p 1050 1738 60 4 v 1050 1826 4 89 v 1106 1826 V 1050 1829 60 4 v 448 2051 a @beginspecial @setspecial @endspecial(W) p 533 2051 a(e) p 605 2051 a(in) m(tro) s(duce) p 1009 2051 a(an) p 1135 2051 a(inner) p 1368 2051 a(pro) s(duct) p 1709 2051 a(on) p Fh 1835 2051 a(L) p Fl 1898 2018 a(2) p Fp 1938 2051 a(:) p Fn 1308 2267 a(<) p 1404 2267 a(A;) p 1512 2267 a(B) p 1611 2267 a(>) p Fm 1682 2286 a(L) p Fc 1731 2267 a(2) p Fp 1769 2267 a(:=) p Fn(<) p 1961 2267 a(\031) p Fp 2016 2267 a(\() p Fn(A) p Fp(\)) p Fn(;) p 2194 2267 a(\031) p Fp 2249 2267 a(\() p Fn(B) p Fp 2358 2267 a(\)) p Fn 2420 2267 a(>) p Fl 2507 2280 a(~) p Fm 2491 2297 a(L) p Fc 2540 2278 a(2) p Fh 448 2482 a(L) p Fl 511 2449 a(2) p Fp 581 2482 a(b) s(ecomes) p 942 2482 a(a) p 1018 2482 a(Hilb) s(ert) p 1332 2482 a(space) p 1574 2482 a(under) p 1832 2482 a(the) p 1989 2482 a(ab) s(o) m(v) m(e) p 2246 2482 a(inner) p 2479 2482 a(pro) s(duct.) p Fe 448 2682 a(Remark) p 846 2682 a(2.3) p 1025 2682 a @beginspecial @setspecial @endspecial Fo(T) p 1083 2682 a(o) p 1172 2682 a(se) p 1246 2682 a(e) p Fh 1332 2682 a(L) p Fl 1395 2649 a(2) p Fo 1477 2682 a(is) p 1585 2682 a(c) p 1622 2682 a(omplete,) p 2000 2682 a(we) p 2146 2682 a(let) p Fh 2284 2682 a(f) p Fn(A) p Fj 2397 2696 a(n) p Fh 2445 2682 a(g) p Fm 2490 2649 a(1) p Fj 2490 2705 a(n) p Fl(=1) p Fh 2672 2682 a(\032) p 2787 2682 a(L) p Fl 2850 2649 a(2) p Fo 2933 2682 a(b) p 2970 2682 a(e) p 3055 2682 a(a) p 3144 2682 a(Cauchy) 448 2806 y(se) p 522 2806 a(quenc) p 743 2806 a(e.) p 855 2806 a(Then) p Fn 1092 2806 a(\031) p Fp 1147 2806 a(\() p Fn(A) p Fj 1250 2820 a(n) p Fp 1297 2806 a(\)\() p Fn(!) s(;) p 1467 2806 a(x) p Fp(\)) p 1581 2806 a(=) p Fn 1677 2806 a(A) p Fj 1745 2820 a(n) p Fp 1792 2806 a(\() p Fn(!) p Fp 1902 2806 a(;) p Fn 1942 2806 a(x;) p Fp 2034 2806 a(0\)) p Fo 2148 2806 a(is) p 2246 2806 a(a) p 2325 2806 a(Cauchy) p 2650 2806 a(se) p 2724 2806 a(quenc) p 2945 2806 a(e) p 3019 2806 a(in) p Fp 3152 2783 a(~) p Fh 3131 2806 a(L) p Fl 3194 2773 a(2) p Fo 3233 2806 a(,) p 3293 2806 a(and) 448 2931 y(thus,) p 678 2931 a(ther) p 829 2931 a(e) p 909 2931 a(exists) p 1163 2931 a(an) p 1298 2931 a(element) p Fn 1640 2931 a(a) p Fp(\() p Fn(!) s(;) p 1823 2931 a(x) p Fp(\)) p Fh 1945 2931 a(2) p Fp 2061 2908 a(~) p Fh 2040 2931 a(L) p Fl 2103 2898 a(2) p Fo 2142 2931 a(,) p 2209 2931 a(such) p 2421 2931 a(that) p Fn 2611 2931 a(\031) p Fp 2666 2931 a(\() p Fn(A) p Fj 2769 2945 a(n) p Fp 2817 2931 a(\)) p Fh 2887 2931 a(!) p Fn 3012 2931 a(a) p Fo 3097 2931 a(in) p Fp 3235 2908 a(~) p Fh 3214 2931 a(L) p Fl 3277 2898 a(2) p Fo 3353 2931 a(as) p Fn 448 3055 a(n) p Fh 543 3055 a(!) p 673 3055 a(1) p Fo(.) p 858 3055 a(We) p 1031 3055 a(de\014ne) p Fn 1303 3055 a(A) p Fp 1411 3055 a(:=) p Fn 1547 3055 a(\031) p Fm 1602 3022 a(\000) p Fl(1) p Fp 1696 3055 a(\() p Fn(a) p Fp(\)) p Fh 1855 3055 a(2) p 1955 3055 a(L) p Fl 2018 3022 a(2) p Fo 2057 3055 a(,) p 2128 3055 a(then) p 2338 3055 a(we) p 2480 3055 a(have) p Fn 2697 3055 a(A) p Fj 2765 3069 a(n) p Fh 2852 3055 a(!) p Fn 2983 3055 a(A) p Fo 3091 3055 a(in) p Fh 3211 3055 a(L) p Fl 3274 3022 a(2) p Fo 3353 3055 a(as) p Fn 448 3180 a(n) p Fh 528 3180 a(!) p 644 3180 a(1) p Fo(.) p 805 3180 a(We) p 970 3180 a(r) p 1003 3180 a(e) p 1040 3180 a(gar) p 1161 3180 a(d) p Fh 1242 3180 a(L) p Fl 1305 3147 a(2) p Fo 1377 3180 a(as) p 1493 3180 a(a) p 1572 3180 a(c) p 1609 3180 a(omplete) p 1946 3180 a(metric) p 2233 3180 a(sp) p 2311 3180 a(ac) p 2394 3180 a(e) p 2470 3180 a(in) p 2581 3180 a(this) p 2755 3180 a(sense.) 589 3379 y @beginspecial @setspecial @endspecial Fp(F) p 640 3379 a(or) p Fn 749 3379 a(A) p Fp(,) p Fn 871 3379 a(B) p Fh 969 3379 a(2) p 1055 3379 a(L) p Fl 1118 3346 a(2) p Fp 1157 3379 a(,) p 1210 3379 a(w) m(e) p 1341 3379 a(de\014ne) p 1600 3379 a(a) p 1673 3379 a(pro) s(duct) p Fn 2011 3379 a(AB) p Fp 2180 3379 a(whic) m(h) p 2437 3379 a(is) p 2525 3379 a(a) p 2597 3379 a(function) p 2950 3379 a(on) p 3073 3379 a(\012) p Fh 3153 3379 a(\002) p Fk 3238 3379 a(Z) p 3258 3379 a(Z) p Fj 3312 3342 a(d) p Fh 3366 3379 a(\002) p Fk 448 3504 a(Z) p 468 3504 a(Z) p Fj 523 3467 a(d) p Fp 564 3504 a(:) 1097 3628 y(\() p Fn(AB) p Fp 1274 3628 a(\)\() p Fn(!) p Fp 1420 3628 a(;) p Fn 1460 3628 a(x;) p 1552 3628 a(y) p Fp 1600 3628 a(\)) p 1661 3628 a(:=) p Fi 1812 3547 a(X) p Fj 1783 3746 a(z) p Fm 1819 3746 a(2) p Fg(Z) p 1882 3746 a(Z) p Ff 1924 3720 a(d) p Fn 1976 3628 a(A) p Fp(\() p Fn(!) p Fp 2154 3628 a(;) p Fn 2194 3628 a(x;) p 2286 3628 a(z) p Fp 2332 3628 a(\)) p Fn(B) p Fp 2441 3628 a(\() p Fn(!) p Fp 2552 3628 a(;) p Fn 2592 3628 a(z) t(;) p 2678 3628 a(y) p Fp 2726 3628 a(\)) p Fn(:) p Fp 448 3628 a(\(2.3\)) 448 3889 y @beginspecial @setspecial @endspecial(If) p Fn 539 3889 a(a) p Fp 613 3889 a(=) p Fn 708 3889 a(\031) p Fp 763 3889 a(\() p Fn(A) p Fp(\),) p Fn 958 3889 a(b) p Fp 1022 3889 a(=) p Fn 1118 3889 a(\031) p Fp 1173 3889 a(\() p Fn(B) p Fp 1282 3889 a(\),) p 1373 3889 a(it) p 1464 3889 a(is) p 1555 3889 a(written) p 1874 3889 a(as) p Fn 1105 4105 a(\031) p Fp 1160 4105 a(\() p Fn(AB) p Fp 1337 4105 a(\)\() p Fn(!) s(;) p 1507 4105 a(x) p Fp(\)) p 1621 4105 a(=) p 1717 4105 a(\() p Fn(AB) p Fp 1894 4105 a(\)\() p Fn(!) p Fp 2040 4105 a(;) p Fn 2080 4105 a(x;) p Fp 2172 4105 a(0\)) p 448 4105 a(\(2.4\)) 1621 4254 y(=) p Fi 1746 4173 a(X) p Fj 1717 4372 a(z) p Fm 1753 4372 a(2) p Fg(Z) p 1816 4372 a(Z) p Ff 1859 4346 a(d) p Fn 1910 4254 a(a) p Fp(\() p Fn(T) p Fm 2059 4216 a(\000) p Fj(z) p Fn 2154 4254 a(!) s(;) p 2254 4254 a(x) p Fh 2326 4254 a(\000) p Fn 2417 4254 a(z) p Fp 2463 4254 a(\)) p Fn(b) p Fp(\() p Fn(!) s(;) p 2672 4254 a(z) p Fp 2718 4254 a(\)) p Fn(:) p Fe 448 4552 a(Lemma) p 819 4552 a(2.1) p 998 4552 a @beginspecial @setspecial @endspecial Fo(The) p 1187 4552 a(sum) p 1384 4552 a(in) p 1498 4552 a(\(2.3\)) p 1730 4552 a(absolutely) p 2149 4552 a(c) p 2186 4552 a(onver) p 2400 4552 a(ges) p 2558 4552 a(for) p 2706 4552 a(a.e.) p Fn 2902 4552 a(!) p Fo 2962 4552 a(.) p 3042 4552 a(Mor) p 3203 4552 a(e) p 3240 4552 a(over,) 448 4677 y(for) p 598 4677 a(any) p 778 4677 a(\014xe) p 908 4677 a(d) p Fp 992 4677 a(\() p Fn(x;) p 1119 4677 a(y) p Fp 1167 4677 a(\)) p Fh 1237 4677 a(2) p Fk 1332 4677 a(Z) p 1351 4677 a(Z) p Fj 1405 4640 a(d) p Fh 1470 4677 a(\002) p Fk 1564 4677 a(Z) p 1583 4677 a(Z) p Fj 1638 4640 a(d) p Fo 1679 4677 a(,) p Fh 1745 4677 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 1949 4677 a(;) p Fn 1989 4677 a(x;) p 2081 4677 a(z) p Fp 2127 4677 a(\)) p Fh(jj) p Fn(B) p Fp 2286 4677 a(\() p Fn(!) p Fp 2398 4677 a(;) p Fn 2438 4677 a(z) t(;) p 2524 4677 a(y) p Fp 2572 4677 a(\)) p Fh(j) p 2667 4677 a(2) p Fn 2762 4677 a(L) p Fl 2824 4644 a(1) p Fp 2863 4677 a(\(\012) p Fh 2988 4677 a(\002) p Fk 3082 4677 a(Z) p 3101 4677 a(Z) p Fj 3156 4640 a(d) p Fp 3197 4677 a(\)) p Fo 3270 4677 a(as) p 3391 4677 a(a) 448 4801 y(function) p 806 4801 a(of) p Fp 913 4801 a(\() p Fn(!) s(;) p 1048 4801 a(z) p Fp 1094 4801 a(\)) p Fh 1155 4801 a(2) p Fp 1241 4801 a(\012) p Fh 1327 4801 a(\002) p Fk 1418 4801 a(Z) p 1437 4801 a(Z) p Fj 1492 4764 a(d) p Fo 1532 4801 a(,) p 1593 4801 a(and) p Fp 1769 4801 a(\() p Fn(AB) p Fp 1946 4801 a(\)\() p Fn(!) p Fp 2092 4801 a(;) p Fn 2132 4801 a(x;) p 2224 4801 a(y) p Fp 2272 4801 a(\)) p Fh 2333 4801 a(2) p Fn 2419 4801 a(L) p Fl 2481 4768 a(1) p Fp 2521 4801 a(\(\012\)) p Fo(.) p Fp 1920 5225 a(8) p eop %%Page: 9 9 9 8 bop 448 573 a @beginspecial @setspecial @endspecial Fo(Pr) p 543 573 a(o) p 584 573 a(of.) p Fh 804 807 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 1008 807 a(;) p Fn 1048 807 a(x;) p 1140 807 a(z) p Fp 1186 807 a(\)) p Fh(jj) p Fn(B) p Fp 1345 807 a(\() p Fn(!) p Fp 1457 807 a(;) p Fn 1497 807 a(z) t(;) p 1583 807 a(y) p Fp 1631 807 a(\)) p Fh(j) p 1717 807 a(\024) p Fp 1823 746 a(1) p 1823 786 46 4 v 1823 869 a(2) p Fi 1879 713 a(\020) p Fh 1928 807 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2132 807 a(;) p Fn 2172 807 a(x;) p 2264 807 a(z) p Fp 2310 807 a(\)) p Fh(j) p Fl 2370 770 a(2) p Fp 2431 807 a(+) p Fh 2522 807 a(j) p Fn(B) p Fp 2621 807 a(\() p Fn(!) p Fp 2731 807 a(;) p Fn 2771 807 a(z) t(;) p 2857 807 a(y) p Fp 2905 807 a(\)) p Fh(j) p Fl 2965 770 a(2) p Fi 3006 713 a(\021) p Fn 3056 807 a(:) p Fp 448 807 a(\(2.5\)) 448 1029 y @beginspecial @setspecial @endspecial(On) p 600 1029 a(the) p 756 1029 a(other) p 994 1029 a(hand,) p Fi 797 1143 a(Z) p Fl 844 1332 a(\012) p Fn 914 1258 a(d) p Fe(P) p Fi 1077 1177 a(X) p Fj 1048 1376 a(z) p Fm 1084 1376 a(2) p Fg(Z) p 1147 1376 a(Z) p Ff 1189 1350 a(d) p Fh 1241 1258 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 1445 1258 a(;) p Fn 1485 1258 a(x;) p 1577 1258 a(z) p Fp 1623 1258 a(\)) p Fh(j) p Fl 1683 1221 a(2) p Fp 1749 1258 a(=) p Fi 1845 1143 a(Z) p Fl 1891 1332 a(\012) p Fn 1961 1258 a(d) p Fe(P) p Fi 2124 1177 a(X) p Fj 2095 1376 a(z) p Fm 2131 1376 a(2) p Fg(Z) p 2194 1376 a(Z) p Ff 2237 1350 a(d) p Fh 2288 1258 a(j) p Fn(A) p Fp(\() p Fn(T) p Fm 2482 1221 a(\000) p Fj(z) p Fn 2577 1258 a(!) p Fp 2652 1258 a(;) p Fn 2692 1258 a(x) p Fh 2765 1258 a(\000) p Fn 2856 1258 a(z) t(;) p Fp 2942 1258 a(0\)) p Fh(j) p Fl 3047 1221 a(2) p Fp 448 1258 a(\(2.6\)) 1749 1536 y(=) p Fi 1845 1421 a(Z) p Fl 1891 1610 a(\012) p Fn 1961 1536 a(d) p Fe(P) p Fi 2124 1456 a(X) p Fj 2095 1654 a(z) p Fm 2131 1654 a(2) p Fg(Z) p 2194 1654 a(Z) p Ff 2237 1629 a(d) p Fh 2288 1536 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2492 1536 a(;) p Fn 2532 1536 a(x) p Fh 2604 1536 a(\000) p Fn 2695 1536 a(z) t(;) p Fp 2781 1536 a(0\)) p Fh(j) p Fl 2886 1499 a(2) p Fp 1749 1815 a(=) p Fi 1845 1700 a(Z) p Fl 1891 1889 a(\012) p Fn 1961 1815 a(d) p Fe(P) p Fi 2124 1734 a(X) p Fj 2095 1933 a(z) p Fm 2131 1933 a(2) p Fg(Z) p 2194 1933 a(Z) p Ff 2237 1907 a(d) p Fh 2288 1815 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2492 1815 a(;) p Fn 2532 1815 a(z) t(;) p Fp 2618 1815 a(0\)) p Fh(j) p Fl 2723 1777 a(2) p Fp 1749 2059 a(=) p Fh 1845 2059 a(k) p Fn(A) p Fh(k) p Fl 2003 2021 a(2) p Fm 2003 2085 a(L) p Fc 2052 2066 a(2) p Fn 2091 2059 a(:) 448 2271 y @beginspecial @setspecial @endspecial Fp(W) p 533 2271 a(e) p 619 2271 a(used) p 841 2271 a(\(CR\)) p 1089 2271 a(prop) s(ert) m(y) p 1475 2271 a(of) p Fn 1593 2271 a(A) p Fp 1705 2271 a(and) p 1896 2271 a(F) p 1947 2271 a(ubini's) p 2256 2271 a(theorem.) p 2688 2271 a(Similarly) p 3040 2271 a(,) p 3110 2271 a(w) m(e) p 3258 2271 a(ha) m(v) m(e) p Fi 448 2327 a(R) p Fl 488 2423 a(\012) p Fn 558 2396 a(d) p Fe(P) p Fi 691 2332 a(P) p Fj 779 2425 a(z) p Fm 815 2425 a(2) p Fg(Z) p 878 2425 a(Z) p Ff 921 2399 a(d) p Fh 976 2396 a(j) p Fn(B) p Fp 1075 2396 a(\() p Fn(!) p Fp 1186 2396 a(;) p Fn 1226 2396 a(z) t(;) p 1312 2396 a(y) p Fp 1360 2396 a(\)) p Fh(j) p Fl 1420 2363 a(2) p Fp 1492 2396 a(=) p Fh 1594 2396 a(k) p Fn(B) p Fh 1713 2396 a(k) p Fl 1758 2363 a(2) p Fm 1758 2427 a(L) p Fc 1807 2408 a(2) p Fn 1876 2396 a(<) p Fh 1978 2396 a(1) p Fp(,) p 2129 2396 a(whic) m(h) p 2393 2396 a(together) p 2755 2396 a(imply) p 3014 2396 a(the) p 3174 2396 a(second) 448 2520 y(statemen) m(t) p 871 2520 a(of) p 974 2520 a(Lemma) p 1299 2520 a(2.1.) p 1481 2520 a(Moreo) m(v) m(er,) p 1906 2520 a(\(2.6\)) p 2123 2520 a(implies) p Fi 2432 2456 a(P) p Fj 2519 2549 a(z) p Fm 2555 2549 a(2) p Fg(Z) p 2618 2549 a(Z) p Ff 2661 2524 a(d) p Fh 2717 2520 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2920 2520 a(;) p Fn 2960 2520 a(x;) p 3052 2520 a(z) p Fp 3098 2520 a(\)) p Fh(j) p Fl 3158 2487 a(2) p Fn 3225 2520 a(<) p Fh 3321 2520 a(1) p Fp(,) 448 2645 y(and) p 621 2645 a(similarly) p 958 2645 a(,) p Fi 1007 2581 a(P) p Fj 1095 2674 a(z) p Fm 1131 2674 a(2) p Fg(Z) p 1194 2674 a(Z) p Ff 1236 2648 a(d) p Fh 1292 2645 a(j) p Fn(B) p Fp 1391 2645 a(\() p Fn(!) p Fp 1501 2645 a(;) p Fn 1541 2645 a(z) t(;) p 1627 2645 a(y) p Fp 1675 2645 a(\)) p Fh(j) p Fl 1735 2612 a(2) p Fn 1801 2645 a(<) p Fh 1897 2645 a(1) p Fp(,) p 2040 2645 a(for) p 2175 2645 a(a.e.) p Fn 2350 2645 a(!) p Fp 2410 2645 a(.) p 2474 2645 a(F) p 2525 2645 a(or) p 2633 2645 a(suc) m(h) p Fn 2834 2645 a(!) p Fh 2919 2645 a(2) p Fp 3005 2645 a(\012,) p 3123 2645 a(the) p 3275 2645 a(sum) 448 2769 y(of) p 552 2769 a(the) p 708 2769 a(RHS) p 924 2769 a(of) p 1028 2769 a(\(2.5\)) p 1245 2769 a(w.r.t.) p Fn 1498 2769 a(z) p Fh 1569 2769 a(2) p Fk 1655 2769 a(Z) p 1675 2769 a(Z) p Fj 1730 2733 a(d) p Fp 1801 2769 a(con) m(v) m(erges,) p 2233 2769 a(and) p Fi 640 2928 a(X) p Fj 611 3126 a(z) p Fm 647 3126 a(2) p Fg(Z) p 710 3126 a(Z) p Ff 753 3101 a(d) p Fh 804 3009 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 1008 3009 a(;) p Fn 1048 3009 a(x;) p 1140 3009 a(z) p Fp 1186 3009 a(\)) p Fh(jj) p Fn(B) p Fp 1345 3009 a(\() p Fn(!) p Fp 1457 3009 a(;) p Fn 1497 3009 a(z) t(;) p 1583 3009 a(y) p Fp 1631 3009 a(\)) p Fh(j) p 1717 3009 a(\024) p Fp 1823 2947 a(1) p 1823 2988 V 1823 3071 a(2) p Fi 1923 2928 a(X) p Fj 1894 3126 a(z) p Fm 1930 3126 a(2) p Fg(Z) p 1993 3126 a(Z) p Ff 2036 3101 a(d) p Fi 2072 2915 a(\020) p Fh 2121 3009 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2325 3009 a(;) p Fn 2365 3009 a(x;) p 2457 3009 a(z) p Fp 2503 3009 a(\)) p Fh(j) p Fl 2563 2971 a(2) p Fp 2624 3009 a(+) p Fh 2715 3009 a(j) p Fn(B) p Fp 2814 3009 a(\() p Fn(!) p Fp 2924 3009 a(;) p Fn 2964 3009 a(z) t(;) p 3050 3009 a(y) p Fp 3098 3009 a(\)) p Fh(j) p Fl 3158 2971 a(2) p Fi 3199 2915 a(\021) p Fn 3249 3009 a(:) p Fp 448 3009 a(\(2.7\)) 448 3311 y @beginspecial @setspecial @endspecial(The) p 635 3311 a(RHS) p 851 3311 a(of) p 955 3311 a(\(2.7\)) p Fh 1172 3311 a(2) p Fn 1258 3311 a(L) p Fl 1320 3278 a(1) p Fp 1359 3311 a(\(\012\),) p 1551 3311 a(and) p 1728 3311 a(th) m(us,) p 1953 3311 a(\() p Fn(AB) p Fp 2130 3311 a(\)\() p Fn(!) p Fp 2276 3311 a(;) p Fn 2316 3311 a(x;) p 2408 3311 a(y) p Fp 2456 3311 a(\)) p Fh 2517 3311 a(2) p Fn 2603 3311 a(L) p Fl 2665 3278 a(1) p Fp 2704 3311 a(\(\012\).) p 2906 3247 60 4 v 2906 3336 4 89 v 2962 3336 V 2906 3339 60 4 v 448 3560 a @beginspecial @setspecial @endspecial(By) p 591 3560 a(using) p 828 3560 a(Lemma) p 1153 3560 a(2.1,) p 1324 3560 a(w) m(e) p 1458 3560 a(can) p 1624 3560 a(sho) m(w) p 1849 3560 a(that) p 2046 3560 a(the) p 2202 3560 a(trace) p 2429 3560 a(p) s(er) p 2588 3560 a(v) m(olume) p Fh 2901 3560 a(T) p Fp 2974 3560 a(\() p Fn(AB) p Fp 3151 3560 a(\)) p 3216 3560 a(exists) 448 3685 y(almost) p 742 3685 a(surely) p 1008 3685 a(if) p Fn 1091 3685 a(A) p Fp(,) p Fn 1215 3685 a(B) p Fh 1314 3685 a(2) p 1399 3685 a(L) p Fl 1462 3652 a(2) p Fp 1501 3685 a(.) p Fe 448 3881 a(Prop) s(osition) p 1014 3881 a(2.2) p 1193 3881 a @beginspecial @setspecial @endspecial Fo(\(1\)) p 1346 3881 a(If) p Fn 1441 3881 a(A) p Fo(,) p Fn 1570 3881 a(B) p Fh 1669 3881 a(2) p 1755 3881 a(L) p Fl 1818 3848 a(2) p Fo 1857 3881 a(,) p Fh 1082 4115 a(T) p Fp 1155 4115 a(\() p Fn(AB) p Fp 1332 4115 a(\)) p 1393 4115 a(=) p Fi 1489 4000 a(Z) p Fl 1535 4189 a(\012) p Fn 1605 4115 a(d) p Fe(P) p Fp(\() p Fn(AB) p Fp 1900 4115 a(\)\() p Fn(!) p Fp 2047 4115 a(;) p 2087 4115 a(0) p Fn(;) p Fp 2172 4115 a(0\)) p Fn(;) p Fo 2387 4115 a(for) p 2532 4115 a(a.e.) p Fn 2718 4115 a(!) s(:) 448 4354 y @beginspecial @setspecial @endspecial Fo(In) p 567 4354 a(p) p 608 4354 a(articular,) p Fh 1011 4354 a(T) p Fp 1083 4354 a(\() p Fn(AB) p Fp 1260 4354 a(\)) p Fo 1328 4354 a(exists) p 1577 4354 a(and) p 1754 4354 a(\014nite) p 1988 4354 a(for) p 2134 4354 a(a.e.) p Fn 2319 4354 a(!) p Fo 2379 4354 a(.) 589 4478 y @beginspecial @setspecial @endspecial(\(2\)) p Fh 743 4478 a(T) p Fp 815 4478 a(\() p Fn(AB) p Fp 992 4478 a(\)) p 1053 4478 a(=) p Fh 1149 4478 a(T) p Fp 1222 4478 a(\() p Fn(B) p 1331 4478 a(A) p Fp(\)) p Fo(,) p 1494 4478 a(for) p 1640 4478 a(a.e.) p Fn 1826 4478 a(!) p Fo 1886 4478 a(.) 448 4727 y @beginspecial @setspecial @endspecial(Pr) p 543 4727 a(o) p 584 4727 a(of.) 589 4852 y @beginspecial @setspecial @endspecial Fp(\(1\)) p 736 4852 a(By) p 879 4852 a(Lemma) p 1204 4852 a(2.1,) p 1376 4852 a(\() p Fn(AB) p Fp 1553 4852 a(\)\() p Fn(!) p Fp 1699 4852 a(;) p Fn 1739 4852 a(x;) p 1831 4852 a(y) p Fp 1879 4852 a(\)) p 1946 4852 a(is) p 2037 4852 a(\014nite) p 2270 4852 a(for) p 2410 4852 a(a.e.) p Fn 2587 4852 a(!) p Fp 2647 4852 a(.) p 2714 4852 a(F) p 2765 4852 a(or) p 2877 4852 a(suc) m(h) p Fn 3083 4852 a(!) p Fh 3168 4852 a(2) p Fp 3255 4852 a(\012,) p 3377 4852 a(it) 448 4976 y(is) p 539 4976 a(clear) p 755 4976 a(that) p 951 4976 a(trace\() p Fn(\037) p Fl 1239 4990 a(\003) p Ff 1288 5001 a(L) p Fn 1340 4976 a(AB) p 1482 4976 a(\037) p Fl 1539 4990 a(\003) p Ff 1588 5001 a(L) p Fp 1638 4976 a(\)) p 1703 4976 a(mak) m(es) p 1975 4976 a(sense) p 2208 4976 a(whic) m(h) p 2467 4976 a(is) p 2557 4976 a(simply) p 2847 4976 a(the) p 3003 4976 a(usual) p 3240 4976 a(trace) 1920 5225 y(9) p eop %%Page: 10 10 10 9 bop Fp 448 573 a(of) p 552 573 a(\(2) p Fn(L) p Fp 715 573 a(+) p 806 573 a(1\)) p Fj 886 540 a(d) p Fh 947 573 a(\002) p Fp 1038 573 a(\(2) p Fn(L) p Fp 1201 573 a(+) p 1292 573 a(1\)) p Fj 1372 540 a(d) p Fp 1443 573 a(matrix) p Fh 1739 573 a(f) p Fp(\() p Fn(AB) p Fp 1961 573 a(\)\() p Fn(!) p Fp 2107 573 a(;) p Fn 2147 573 a(x;) p 2239 573 a(y) p Fp 2287 573 a(\)) p Fh(g) p Fj 2367 587 a(x;y) p Fm 2464 587 a(2) p Fl(\003) p Ff 2560 598 a(L) p Fp 2612 573 a(.) p Fh 1180 782 a(T) p Fp 1252 782 a(\() p Fn(AB) p Fp 1429 782 a(\)) p 1490 782 a(=) p 1600 782 a(lim) p Fj 1586 842 a(L) p Fm("1) p Fp 1825 721 a(1) p 1765 761 166 4 v Fh 1765 845 a(j) p Fp(\003) p Fj 1853 859 a(L) p Fh 1905 845 a(j) p Fp 1941 782 a(trace) q(\() p Fn(\037) p Fl 2230 796 a(\003) p Ff 2279 807 a(L) p Fn 2329 782 a(AB) p 2471 782 a(\037) p Fl 2528 796 a(\003) p Ff 2577 807 a(L) p Fp 2627 782 a(\)) p 448 782 a(\(2.8\)) 1490 1021 y(=) p 1600 1021 a(lim) p Fj 1586 1081 a(L) p Fm("1) p Fp 1825 959 a(1) p 1765 1000 V Fh 1765 1083 a(j) p Fp(\003) p Fj 1853 1097 a(L) p Fh 1905 1083 a(j) p Fi 1987 940 a(X) p Fj 1956 1124 a(x) p Fm(2) p Fl(\003) p Ff 2092 1135 a(L) p Fp 2138 1021 a(\() p Fn(AB) p Fp 2315 1021 a(\)\() p Fn(!) p Fp 2460 1021 a(;) p Fn 2500 1021 a(x;) p 2592 1021 a(x) p Fp(\)) p Fn(:) 448 1281 y @beginspecial @setspecial @endspecial Fp(On) p 600 1281 a(the) p 756 1281 a(other) p 994 1281 a(hand,) p 1247 1281 a(b) m(y) p 1373 1281 a(using) p 1611 1281 a(\(CR\)) p 1844 1281 a(prop) s(ert) m(y) p 2216 1281 a(of) p Fh 2320 1281 a(L) p Fl 2383 1248 a(2) p Fp 2422 1281 a(,) 795 1460 y(\() p Fn(AB) p Fp 972 1460 a(\)\() p Fn(!) p Fp 1118 1460 a(;) p Fn 1158 1460 a(x;) p 1250 1460 a(x) p Fp(\)) p 1363 1460 a(=) p Fi 1489 1379 a(X) p Fj 1459 1577 a(y) p Fm 1496 1577 a(2) p Fg(Z) p 1559 1577 a(Z) p Ff 1602 1552 a(d) p Fn 1654 1460 a(A) p Fp(\() p Fn(!) p Fp 1832 1460 a(;) p Fn 1872 1460 a(x;) p 1964 1460 a(y) p Fp 2012 1460 a(\)) p Fn(B) p Fp 2121 1460 a(\() p Fn(!) p Fp 2232 1460 a(;) p Fn 2272 1460 a(y) s(;) p 2360 1460 a(x) p Fp(\)) p 448 1460 a(\(2.9\)) 1363 1721 y(=) p Fi 1489 1640 a(X) p Fj 1459 1839 a(y) p Fm 1496 1839 a(2) p Fg(Z) p 1559 1839 a(Z) p Ff 1602 1813 a(d) p Fn 1654 1721 a(A) p Fp(\() p Fn(T) p Fm 1823 1683 a(\000) p Fj(x) p Fn 1922 1721 a(!) p Fp 1997 1721 a(;) p 2037 1721 a(0) p Fn(;) p 2122 1721 a(y) p Fh 2191 1721 a(\000) p Fn 2282 1721 a(x) p Fp(\)) p Fn(B) p Fp 2443 1721 a(\() p Fn(T) p Fm 2544 1683 a(\000) p Fj(x) p Fn 2643 1721 a(!) p Fp 2718 1721 a(;) p Fn 2758 1721 a(y) p Fh 2826 1721 a(\000) p Fn 2917 1721 a(x;) p Fp 3009 1721 a(0\)) 1363 1971 y(=) p 1459 1971 a(\() p Fn(AB) p Fp 1636 1971 a(\)\() p Fn(T) p Fm 1772 1933 a(\000) p Fj(x) p Fn 1871 1971 a(!) p Fp 1946 1971 a(;) p 1986 1971 a(0) p Fn(;) p Fp 2071 1971 a(0\)) p Fn(:) 448 2149 y @beginspecial @setspecial @endspecial Fp(By) p 593 2149 a(Lemma) p 919 2149 a(2.1,) p 1094 2149 a(the) p 1252 2149 a(RHS) p 1470 2149 a(of) p 1576 2149 a(\(2.9\)) p Fh(2) p Fn 1852 2149 a(L) p Fl 1914 2116 a(1) p Fp 1953 2149 a(\(\012\).) p 2161 2149 a(Therefore,) p 2601 2149 a(b) m(y) p 2729 2149 a(Birkho\013) p 3059 2149 a('s) p 3152 2149 a(ergo) s(dic) 448 2274 y(theorem,) p Fh 1091 2415 a(T) p Fp 1164 2415 a(\() p Fn(AB) p Fp 1341 2415 a(\)) p 1401 2415 a(=) p Fi 1497 2300 a(Z) p Fl 1543 2489 a(\012) p Fn 1614 2415 a(d) p Fe(P) p Fp(\() p Fn(AB) p Fp 1909 2415 a(\)\() p Fn(!) p Fp 2055 2415 a(;) p 2095 2415 a(0) p Fn(;) p Fp 2180 2415 a(0\)) p Fn(;) p Fp 2393 2415 a(for) p 2533 2415 a(a.e.) p Fn 2709 2415 a(!) s(:) 589 2600 y @beginspecial @setspecial @endspecial Fp(\(2\)) p 736 2600 a(F) p 787 2600 a(or) p 899 2600 a(a.e.) p Fn 1076 2600 a(!) p Fp 1136 2600 a(,) p Fh 1007 2800 a(T) p Fp 1079 2800 a(\() p Fn(AB) p Fp 1256 2800 a(\)) p 1317 2800 a(=) p Fi 1413 2685 a(Z) p Fl 1459 2874 a(\012) p Fn 1529 2800 a(d) p Fe(P) p Fp(\() p Fn(AB) p Fp 1824 2800 a(\)\() p Fn(!) p Fp 1971 2800 a(;) p 2011 2800 a(0) p Fn(;) p Fp 2096 2800 a(0\)) p 448 2800 a(\(2.10\)) 1317 3022 y(=) p Fi 1413 2907 a(Z) p Fl 1459 3096 a(\012) p Fn 1529 3022 a(d) p Fe(P) p Fi 1693 2941 a(X) p Fj 1663 3140 a(y) p Fm 1700 3140 a(2) p Fg(Z) p 1763 3140 a(Z) p Ff 1807 3114 a(d) p Fn 1858 3022 a(A) p Fp(\() p Fn(!) p Fp 2036 3022 a(;) p 2076 3022 a(0) p Fn(;) p 2161 3022 a(y) p Fp 2209 3022 a(\)) p Fn(B) p Fp 2318 3022 a(\() p Fn(!) p Fp 2430 3022 a(;) p Fn 2470 3022 a(y) s(;) p Fp 2558 3022 a(0\)) 1317 3309 y(=) p Fi 1413 3194 a(Z) p Fl 1459 3383 a(\012) p Fn 1529 3309 a(d) p Fe(P) p Fi 1693 3229 a(X) p Fj 1663 3427 a(y) p Fm 1700 3427 a(2) p Fg(Z) p 1763 3427 a(Z) p Ff 1807 3402 a(d) p Fn 1858 3309 a(B) p Fp 1932 3309 a(\() p Fn(T) p Fj 2033 3272 a(y) p Fn 2074 3309 a(!) p Fp 2149 3309 a(;) p 2189 3309 a(0) p Fn(;) p 2274 3309 a(y) p Fp 2322 3309 a(\)) p Fn(A) p Fp(\() p Fn(T) p Fj 2526 3272 a(y) p Fn 2569 3309 a(!) p Fp 2644 3309 a(;) p Fn 2684 3309 a(y) s(;) p Fp 2772 3309 a(0\)) p Fn(:) 448 3594 y @beginspecial @setspecial @endspecial Fp(By) p 599 3594 a(Lemma) p 931 3594 a(2.1,) p Fh 1112 3594 a(j) p Fn(B) p Fp 1211 3594 a(\() p Fn(!) p Fp 1321 3594 a(;) p 1361 3594 a(0) p Fn(;) p 1446 3594 a(y) p Fp 1494 3594 a(\)) p Fh(jj) p Fn(A) p Fp(\() p Fn(!) p Fp 1760 3594 a(;) p Fn 1800 3594 a(y) s(;) p Fp 1888 3594 a(0\)) p Fh(j) p 2033 3594 a(2) p Fn 2131 3594 a(L) p Fl 2193 3561 a(1) p Fp 2232 3594 a(\(\012) p Fh 2359 3594 a(\002) p Fk 2455 3594 a(Z) p 2475 3594 a(Z) p Fj 2530 3557 a(d) p Fp 2570 3594 a(\),) p 2671 3594 a(so) p 2790 3594 a(that) p 2994 3594 a(w) m(e) p 3136 3594 a(can) p 3310 3594 a(use) 448 3718 y(F) p 499 3718 a(ubini's) p 794 3718 a(theorem.) 993 3897 y(RHS) p 1209 3897 a(of) p 1313 3897 a(\(2.10\)) p 1570 3897 a(=) p Fi 1696 3816 a(X) p Fj 1666 4014 a(y) p Fm 1703 4014 a(2) p Fg(Z) p 1766 4014 a(Z) p Ff 1809 3989 a(d) p Fi 1861 3782 a(Z) p Fl 1907 3970 a(\012) p Fn 1977 3897 a(d) p Fe(P) p Fn(B) p Fp 2169 3897 a(\() p Fn(!) p Fp 2280 3897 a(;) p 2320 3897 a(0) p Fn(;) p 2405 3897 a(y) p Fp 2453 3897 a(\)) p Fn(A) p Fp(\() p Fn(!) p Fp 2668 3897 a(;) p Fn 2708 3897 a(y) s(;) p Fp 2796 3897 a(0\)) 1570 4184 y(=) p Fi 1666 4069 a(Z) p Fl 1712 4258 a(\012) p Fn 1782 4184 a(d) p Fe(P) p Fi 1946 4103 a(X) p Fj 1916 4302 a(y) p Fm 1953 4302 a(2) p Fg(Z) p 2016 4302 a(Z) p Ff 2060 4276 a(d) p Fn 2111 4184 a(B) p Fp 2185 4184 a(\() p Fn(!) p Fp 2295 4184 a(;) p 2335 4184 a(0) p Fn(;) p 2420 4184 a(y) p Fp 2468 4184 a(\)) p Fn(A) p Fp(\() p Fn(!) p Fp 2683 4184 a(;) p Fn 2723 4184 a(y) s(;) p Fp 2811 4184 a(0\)) 1570 4424 y(=) p Fh 1666 4424 a(T) p Fp 1739 4424 a(\() p Fn(B) p 1848 4424 a(A) p Fp(\)) p Fn(:) p 448 4539 60 4 v 448 4628 4 89 v 504 4628 V 448 4631 60 4 v 448 4852 a @beginspecial @setspecial @endspecial Fp(W) p 533 4852 a(e) p 610 4852 a(ha) m(v) m(e) p 825 4852 a(the) p 987 4852 a(follo) m(wing) p 1376 4852 a(fact,) p 1587 4852 a(whic) m(h) p 1852 4852 a(will) p 2029 4852 a(mak) m(e) p 2271 4852 a(it) p 2367 4852 a(easier) p 2626 4852 a(to) p 2742 4852 a(study) p 2998 4852 a(un) m(b) s(ounded) 448 4976 y(op) s(erators) p 851 4976 a(on) p Fh 977 4976 a(L) p Fl 1040 4943 a(2) p Fp 1079 4976 a(.) 1897 5225 y(10) p eop %%Page: 11 11 11 10 bop Fe 448 573 a(Prop) s(osition) p 1014 573 a(2.3) p 1193 573 a @beginspecial @setspecial @endspecial Fh(A) p Fo 1298 573 a(is) p 1395 573 a(dense) p 1646 573 a(in) p Fh 1758 573 a(L) p Fl 1821 540 a(2) p Fo 1860 573 a(.) 448 822 y @beginspecial @setspecial @endspecial(Pr) p 543 822 a(o) p 584 822 a(of.) p Fp 728 822 a(Let) p Fn 891 822 a(A) p Fh 984 822 a(2) p 1070 822 a(L) p Fl 1133 789 a(2) p Fp 1172 822 a(,) p Fn 1228 822 a(a) p Fp 1301 822 a(:=) p Fn 1422 822 a(\031) p Fp 1477 822 a(\() p Fn(A) p Fp(\)) p Fh 1642 822 a(2) p Fp 1749 799 a(~) p Fh 1728 822 a(L) p Fl 1791 789 a(2) p Fp 1830 822 a(.) p 1895 822 a(De\014ne) p Fn 870 1027 a(a) p Fj 918 1041 a(n) p Fp 965 1027 a(\() p Fn(!) s(;) p 1100 1027 a(x) p Fp(\)) p 1213 1027 a(:=) p Fi 1334 908 a(\032) p Fn 1411 971 a(a) p Fp(\() p Fn(!) s(;) p 1594 971 a(x) p Fp(\)) p Fn(;) p Fp 1799 971 a(\(if) p Fh 1917 971 a(j) p Fn(x) p Fh(j) p 2045 971 a(\024) p Fn 2141 971 a(n) p Fp 2226 971 a(and) p Fh 2403 971 a(j) p Fn(a) p Fp(\() p Fn(!) s(;) p 2611 971 a(x) p Fp(\)) p Fh(j) p 2749 971 a(\024) p Fn 2845 971 a(n) p Fp(\),) 1411 1084 y(0) p Fn(;) p Fp 1799 1084 a(\(otherwise\),) p Fn 1072 1220 a(A) p Fj 1140 1234 a(n) p Fp 1213 1220 a(:=) p Fn 1334 1220 a(\031) p Fm 1389 1182 a(\000) p Fl(1) p Fp 1483 1220 a(\() p Fn(a) p Fj 1566 1234 a(n) p Fp 1614 1220 a(\)) p Fn(:) 448 1394 y @beginspecial @setspecial @endspecial Fp(Then) p Fn 689 1394 a(a) p Fj 737 1408 a(n) p Fh 814 1394 a(!) p Fn 935 1394 a(a) p Fp(,) p 1043 1394 a(and) p Fn 1223 1394 a(A) 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1346 2072 a(2) p Fh 1387 2110 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 1590 2110 a(;) p Fn 1630 2110 a(x;) p 1722 2110 a(y) p Fp 1770 2110 a(\)) p Fh(j) p Fi 1830 2016 a(\021) p Fl 1881 2039 a(1) p Fj(=) p Fl(2) p Fi 1991 2016 a(\020) 2100 2029 y(X) p Fj 2041 2228 a(x;y) p Fm 2138 2228 a(2) p Fg(Z) p 2201 2228 a(Z) p Ff 2243 2202 a(d) p Fh 2295 2110 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2499 2110 a(;) p Fn 2539 2110 a(x;) p 2631 2110 a(y) p Fp 2679 2110 a(\)) p Fh(jj) p Fn( ) p Fp 2826 2110 a(\() p Fn(y) p Fp 2909 2110 a(\)) p Fh(j) p Fl 2969 2072 a(2) p Fi 3011 2016 a(\021) p Fl 3060 2039 a(1) p Fj(=) p Fl(2) p Fp 715 2403 a(=) p Fi 811 2309 a(\020) 892 2322 y(X) p Fj 861 2521 a(x) p Fm(2) p Fg(Z) p 964 2521 a(Z) p Ff 1006 2495 a(d) p Fi 1087 2322 a(X) p Fj 1058 2521 a(y) p Fm 1095 2521 a(2) p Fg(Z) p 1158 2521 a(Z) p Ff 1201 2495 a(d) p Fh 1252 2403 a(j) p Fn(') p Fp(\() p Fn(x) p Fp(\)) p Fh(j) p Fl 1483 2366 a(2) p Fh 1524 2403 a(j) p Fn(a) p Fj 1597 2417 a(n) p Fp 1645 2403 a(\() p Fn(T) p Fm 1746 2366 a(\000) p Fj(y) p Fn 1842 2403 a(!) s(;) p 1942 2403 a(x) p Fh 2014 2403 a(\000) p Fn 2105 2403 a(y) p Fp 2153 2403 a(\)) p Fh(j) p Fi 2213 2309 a(\021) p Fl 2263 2332 a(1) p Fj(=) p Fl(2) p Fh 2394 2403 a(\002) 1079 2696 y(\002) p Fi 1150 2602 a(\020) 1229 2615 y(X) p Fj 1199 2814 a(y) p Fm 1236 2814 a(2) p Fg(Z) p 1299 2814 a(Z) p Ff 1342 2788 a(d) p Fi 1425 2615 a(X) p Fj 1394 2814 a(x) p Fm(2) p Fg(Z) p 1497 2814 a(Z) p Ff 1539 2788 a(d) p Fh 1591 2696 a(j) p Fn(a) p Fj 1664 2710 a(n) p Fp 1711 2696 a(\() p Fn(T) p Fm 1812 2659 a(\000) p Fj(y) p Fn 1908 2696 a(!) s(;) p 2008 2696 a(x) p Fh 2081 2696 a(\000) p Fn 2172 2696 a(y) p Fp 2220 2696 a(\)) p Fh(jj) p Fn( ) p Fp 2367 2696 a(\() p Fn(y) p Fp 2450 2696 a(\)) p Fh(j) p Fl 2510 2659 a(2) p Fi 2551 2602 a(\021) p Fl 2601 2625 a(1) p Fj(=) p Fl(2) p Fn 2711 2696 a(:) 448 2966 y @beginspecial @setspecial @endspecial Fp(W) p 533 2966 a(e) p 614 2966 a(notice) p 891 2966 a(that,) p Fh 1125 2966 a(j) p Fn(a) p Fj 1198 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3442 a(j) p Fn(') p Fp(\() p Fn(x) p Fp(\)) p Fh(j) p Fl 1792 3404 a(2) p Fi 1833 3347 a(\021) p Fl 1882 3370 a(1) p Fj(=) p Fl(2) p Fi 1992 3347 a(\020) p Fn 2042 3442 a(n) p Fp(\(2) p Fn(n) p Fp 2252 3442 a(+) p 2343 3442 a(1\)) p Fj 2423 3404 a(d) p Fi 2509 3361 a(X) p Fj 2480 3559 a(y) p Fm 2517 3559 a(2) p Fg(Z) p 2580 3559 a(Z) p Ff 2623 3534 a(d) p Fh 2674 3442 a(j) p Fn( ) p Fp 2761 3442 a(\() p Fn(y) p Fp 2844 3442 a(\)) p Fh(j) p Fl 2904 3404 a(2) p Fi 2945 3347 a(\021) p Fl 2995 3370 a(1) p Fj(=) p Fl(2) p Fp 781 3682 a(=) p Fn 877 3682 a(C) p Fj 942 3696 a(n) p Fh 989 3682 a(k) p Fn(') p Fh(k) p Fj 1138 3711 a(l) p Fc 1160 3692 a(2) p Fl 1195 3711 a(\() p Fg(Z) p 1238 3711 a(Z) p Ff 1282 3685 a(d) p Fl 1318 3711 a(\)) p Fh 1350 3682 a(k) p Fn( ) p Fh 1457 3682 a(k) p Fj 1502 3711 a(l) p Fc 1524 3692 a(2) p Fl 1559 3711 a(\() p Fg(Z) p 1602 3711 a(Z) p Ff 1646 3685 a(d) p Fl 1682 3711 a(\)) p Fn 1714 3682 a(;) 448 3856 y @beginspecial @setspecial @endspecial Fp(where) p 724 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1202 573 a(Prop) s(osition) p 1697 573 a(2.3) p 1848 573 a(also) p 2035 573 a(sho) m(ws) p Fh 2301 573 a(A) p Fl 2374 587 a(0) p Fh 2446 573 a(\032) p 2550 573 a(A) p Fp(,) p 2684 573 a(and) p Fh 2865 573 a(A) p Fl 2938 587 a(0) p Fp 3012 573 a(is) p 3109 573 a(dense) p 3361 573 a(in) p Fh 448 697 a(L) p Fl 511 664 a(2) p Fp 550 697 a(.) 589 822 y @beginspecial @setspecial @endspecial(F) p 640 822 a(rom) p 847 822 a(no) m(w) p 1056 822 a(on,) p 1231 822 a(w) m(e) p 1383 822 a(consider) p 1757 822 a(some) p 2003 822 a(op) s(erations) p 2465 822 a(on) p Fh 2610 822 a(L) p Fl 2673 789 a(2) p Fp 2712 822 a(.) p 2835 822 a(F) p 2886 822 a(or) p 3017 822 a(a) p 3111 822 a(function) p Fn 448 946 a(A) p Fp(\() p Fn(!) p Fp 627 946 a(;) p Fn 667 946 a(x;) p 759 946 a(y) p Fp 807 946 a(\)) p 873 946 a(on) p 999 946 a(\012) p Fh 1085 946 a(\002) p Fk 1176 946 a(Z) p 1196 946 a(Z) p Fj 1251 910 a(d) p Fh 1312 946 a(\002) p Fk 1402 946 a(Z) p 1422 946 a(Z) p Fj 1477 910 a(d) p Fp 1518 946 a(,) p 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4892 a(y) p Fp 2770 4892 a(\)) 1897 5225 y(12) p eop %%Page: 13 13 13 12 bop Fp 1651 573 a(=) p Fi 1776 492 a(X) p Fj 1747 691 a(z) p Fm 1783 691 a(2) p Fg(Z) p 1846 691 a(Z) p Ff 1889 665 a(d) p 1940 495 393 4 v Fn 1940 573 a(A) p Fp(\() p Fn(!) p Fp 2119 573 a(;) p Fn 2159 573 a(z) t(;) p 2245 573 a(x) p Fp(\)) p 2348 495 395 4 v Fn 2348 573 a(B) p Fp 2422 573 a(\() p Fn(!) p Fp 2532 573 a(;) p Fn 2572 573 a(y) s(;) p 2660 573 a(z) p Fp 2706 573 a(\)) 1651 805 y(=) p 1747 805 a(\() p Fn(B) p 1856 805 a(A) p Fp(\)) p Fm 1959 767 a(\003) p Fp 1999 805 a(\() p Fn(!) p Fp 2110 805 a(;) p Fn 2150 805 a(x;) p 2242 805 a(y) p Fp 2290 805 a(\)) p Fn(:) 448 972 y @beginspecial @setspecial @endspecial Fp(By) p 591 972 a(Lemma) p 915 972 a(2.1,) p 1087 972 a(the) p 1244 972 a(ab) s(o) m(v) m(e) p 1501 972 a(sums) p 1730 972 a(absolutely) p 2162 972 a(con) m(v) m(erge) p 2533 972 a(for) p 2673 972 a(a.e.) p Fn 2849 972 a(!) p Fp 2909 972 a(.) 589 1096 y @beginspecial @setspecial @endspecial(\(2\)) p 736 1096 a(By) p 879 1096 a(Prop) s(osition) p 1368 1096 a(2.2,) p Fh 1081 1285 a(T) p Fp 1154 1285 a(\() p Fn(A) p Fm 1257 1247 a(\003) p Fn 1297 1285 a(B) p Fp 1371 1285 a(\)) p 1431 1285 a(=) p Fi 1527 1170 a(Z) p Fl 1573 1358 a(\012) p Fn 1643 1285 a(d) p Fe(P) p Fi 1808 1204 a(X) p Fj 1777 1402 a(x) p Fm(2) p Fg(Z) p 1880 1402 a(Z) p Ff 1923 1377 a(d) p Fn 1974 1285 a(A) p Fm 2042 1247 a(\003) p Fp 2082 1285 a(\() p Fn(!) p Fp 2192 1285 a(;) p 2232 1285 a(0) p Fn(;) p 2317 1285 a(x) p Fp(\)) p Fn(B) p Fp 2478 1285 a(\() p Fn(!) p Fp 2590 1285 a(;) p Fn 2630 1285 a(x;) p Fp 2722 1285 a(0\)) 1431 1563 y(=) p Fi 1527 1448 a(Z) p Fl 1573 1637 a(\012) p Fn 1643 1563 a(d) p Fe(P) p Fi 1808 1482 a(X) p Fj 1777 1681 a(x) p Fm(2) p Fg(Z) p 1880 1681 a(Z) p Ff 1923 1655 a(d) p 1974 1485 393 4 v Fn 1974 1563 a(A) p Fp(\() p Fn(!) p Fp 2153 1563 a(;) p Fn 2193 1563 a(x;) p Fp 2285 1563 a(0\)) p Fn 2382 1563 a(B) p Fp 2456 1563 a(\() p Fn(!) p Fp 2565 1563 a(;) p Fn 2605 1563 a(x;) p Fp 2697 1563 a(0\)) p Fn(;) 448 1812 y @beginspecial @setspecial @endspecial Fp(for) p 587 1812 a(a.e.) p Fn 764 1812 a(!) p Fp 824 1812 a(.) p 890 1812 a(Therefore,) p 1327 1812 a(since) p Fn 1550 1812 a(A) p Fp(\() p Fn(!) p Fp 1728 1812 a(;) p Fn 1768 1812 a(x;) p Fp 1860 1812 a(0\)) p 1967 1812 a(=) p Fn 2063 1812 a(\031) p Fp 2118 1812 a(\() p Fn(A) p Fp(\),) p Fh 1351 1979 a(T) p Fp 1423 1979 a(\() p Fn(A) p Fm 1526 1941 a(\003) p Fn 1566 1979 a(B) p Fp 1640 1979 a(\)) p 1701 1979 a(=) p Fn(<) p 1867 1979 a(\031) p Fp 1922 1979 a(\() p Fn(A) p Fp(\)) p Fn(;) p 2100 1979 a(\031) p Fp 2155 1979 a(\() p Fn(B) p Fp 2264 1979 a(\)) p Fn 2326 1979 a(>) p Fl 2413 1992 a(~) p Fm 2397 2009 a(L) p Fc 2446 1990 a(2) p Fn 2509 1979 a(:) p 448 2082 60 4 v 448 2171 4 89 v 504 2171 V 448 2174 60 4 v 448 2395 a @beginspecial @setspecial @endspecial Fp(The) p 635 2395 a(follo) m(wing) p 1019 2395 a(ideal) p 1236 2395 a(prop) s(ert) m(y) p 1608 2395 a(of) p Fh 1711 2395 a(L) p Fl 1774 2362 a(2) p Fp 1844 2395 a(will) p 2016 2395 a(b) s(e) p 2139 2395 a(used) p 2347 2395 a(frequen) m(tly) p 2776 2395 a(in) p 2883 2395 a(this) p 3060 2395 a(pap) s(er.) p Fe 448 2554 a(Prop) s(osition) p 1014 2554 a(2.5) p 1193 2554 a @beginspecial @setspecial @endspecial Fo(\(1\)) p 1353 2554 a(L) p 1405 2554 a(et) p Fn 1518 2554 a(A) p Fh 1625 2554 a(2) p 1724 2554 a(L) p Fl 1787 2521 a(2) p Fo 1826 2554 a(,) p Fn 1896 2554 a(B) p Fh 2008 2554 a(2) p 2107 2554 a(A) p Fo(.) p 2272 2554 a(Sinc) p 2439 2554 a(e) p Fn 2521 2554 a(B) p Fh 2633 2554 a(2) p 2733 2554 a(A) p 2844 2554 a(\032) p 2953 2554 a(L) p Fl 3016 2521 a(2) p Fo 3095 2554 a(\(R) p 3193 2554 a(emark) 448 2678 y(2.2\),) p 669 2678 a(we) p 806 2678 a(c) p 843 2678 a(an) p 976 2678 a(de\014ne) p 1243 2678 a(pr) p 1322 2678 a(o) p 1363 2678 a(ducts) p Fn 1604 2678 a(B) p 1678 2678 a(A) p Fo(,) p Fn 1809 2678 a(AB) p Fo 1985 2678 a(as) p 2104 2678 a(functions) p 2501 2678 a(on) p Fp 2633 2678 a(\012) p Fh 2721 2678 a(\002) p Fk 2813 2678 a(Z) p 2832 2678 a(Z) p Fj 2887 2641 a(d) p Fh 2949 2678 a(\002) p Fk 3042 2678 a(Z) p 3061 2678 a(Z) p Fj 3116 2641 a(d) p Fo 3156 2678 a(.) p 3233 2678 a(Then) p Fn 448 2803 a(B) p 522 2803 a(A) p Fo(,) p Fn 650 2803 a(AB) p Fh 817 2803 a(2) p 903 2803 a(L) p Fl 966 2770 a(2) p Fo 1005 2803 a(,) p 1066 2803 a(and) p Fh 1167 2970 a(k) p Fn(B) p 1286 2970 a(A) p Fh(k) p Fm 1399 2989 a(L) p Fc 1448 2970 a(2) p Fp 1512 2970 a(=) p Fh 1608 2970 a(k) p Fn(AB) p Fh 1795 2970 a(k) p Fm 1840 2989 a(L) p Fc 1889 2970 a(2) p Fh 1953 2970 a(\024) p Fp 2053 2970 a(sup) p Fj 2049 3046 a(!) p Fm 2095 3046 a(2) p Fl(\012) p Fh 2209 2970 a(k) p Fn(B) p Fh 2328 2970 a(k) p Fj 2373 2984 a(op) p Fh 2447 2970 a(k) p Fn(A) p Fh(k) p Fm 2605 2989 a(L) p Fc 2654 2970 a(2) p Fn 2693 2970 a(:) 448 3185 y @beginspecial @setspecial @endspecial Fo(Henc) p 646 3185 a(e) p 719 3185 a(the) p 869 3185 a(multiplic) p 1207 3185 a(ation) p 1442 3185 a(op) p 1529 3185 a(er) p 1604 3185 a(ators) p 1836 3185 a(on) p Fh 1965 3185 a(L) p Fl 2028 3152 a(2) p Fo 2099 3185 a(de\014ne) p 2326 3185 a(d) p 2404 3185 a(by) p Fn 2522 3185 a(A) p Fh 2615 3185 a(7!) p Fn 2731 3185 a(B) p 2805 3185 a(A) p Fo(,) p Fn 2932 3185 a(A) p Fh 3026 3185 a(7!) p Fn 3142 3185 a(AB) p Fo 3315 3185 a(ar) p 3394 3185 a(e) 448 3310 y(line) p 587 3310 a(ar) p 705 3310 a(and) p 882 3310 a(b) p 919 3310 a(ounde) p 1148 3310 a(d.) 589 3434 y @beginspecial @setspecial @endspecial(\(2\)) p 750 3434 a(The) p 944 3434 a(adjoint) p 1260 3434 a(op) p 1347 3434 a(er) p 1422 3434 a(ators) p 1663 3434 a(of) p Fn 1777 3434 a(A) p Fh 1884 3434 a(7!) p Fn 2014 3434 a(B) p 2088 3434 a(A) p Fo(,) p Fn 2225 3434 a(A) p Fh 2332 3434 a(7!) p Fn 2462 3434 a(AB) p Fo 2643 3434 a(ar) p 2722 3434 a(e) p Fn 2805 3434 a(A) p Fh 2912 3434 a(7!) p Fn 3042 3434 a(B) p Fm 3116 3401 a(\003) p Fn 3155 3434 a(A) p Fo(,) p 3293 3434 a(and) p Fn 448 3559 a(A) p Fh 542 3559 a(7!) p Fn 658 3559 a(AB) p Fm 800 3526 a(\003) p Fo 872 3559 a(r) p 905 3559 a(esp) p 1025 3559 a(e) p 1062 3559 a(ctively.) 448 3808 y @beginspecial @setspecial @endspecial(Pr) p 543 3808 a(o) p 584 3808 a(of.) p Fp 796 3808 a(\(1\)) p 965 3808 a(By) p 1131 3808 a(Lemma) p 1478 3808 a(2.1,) p 1678 3808 a(\() p Fn(B) p 1787 3808 a(A) p Fp(\)\() p Fn(!) p Fp 2001 3808 a(;) p Fn 2041 3808 a(x;) p 2133 3808 a(y) p Fp 2181 3808 a(\)) p 2270 3808 a(and) p 2469 3808 a(\() p Fn(AB) p Fp 2646 3808 a(\)\() p Fn(!) p Fp 2792 3808 a(;) p Fn 2832 3808 a(x;) p 2924 3808 a(y) p Fp 2972 3808 a(\)) p 3061 3808 a(are) p 3235 3808 a(\014nite) 448 3933 y(a.e.) p 648 3933 a(It) p 754 3933 a(is) p 853 3933 a(easy) p 1061 3933 a(to) p 1180 3933 a(see) p 1334 3933 a(\() p Fn(B) p 1443 3933 a(A) p Fp(\)\() p Fn(!) p Fp 1657 3933 a(;) p Fn 1697 3933 a(x;) p 1789 3933 a(y) p Fp 1837 3933 a(\)) p 1911 3933 a(and) p 2095 3933 a(\() p Fn(AB) p Fp 2272 3933 a(\)\() p Fn(!) p Fp 2418 3933 a(;) p Fn 2458 3933 a(x;) p 2550 3933 a(y) p Fp 2598 3933 a(\)) p 2672 3933 a(satisfy) p 2964 3933 a(\(CR\).) p 3230 3933 a(Since) p Fi 448 3988 a(R) p Fl 488 4085 a(\012) p Fn 558 4057 a(d) p Fe(P) p Fi 691 3993 a(P) p Fj 779 4086 a(x) p Fm(2) p Fg(Z) p 882 4086 a(Z) p Ff 925 4060 a(d) p Fh 981 4057 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 1184 4057 a(;) p Fn 1224 4057 a(x;) p Fp 1316 4057 a(0\)) p Fh(j) p Fl 1421 4024 a(2) p Fp 1491 4057 a(=) p Fh 1590 4057 a(k) p Fn(A) p Fh(k) p Fl 1748 4024 a(2) p Fm 1748 4088 a(L) p Fc 1797 4070 a(2) p Fn 1865 4057 a(<) p Fh 1964 4057 a(1) p Fp(,) p Fi 2113 3993 a(P) p Fj 2200 4086 a(x) p Fm(2) p Fg(Z) p 2303 4086 a(Z) p Ff 2346 4060 a(d) p Fh 2401 4057 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2605 4057 a(;) p Fn 2645 4057 a(x;) p Fp 2737 4057 a(0\)) p Fh(j) p Fl 2842 4024 a(2) p Fn 2912 4057 a(<) p Fh 3011 4057 a(1) p Fp(,) p 3160 4057 a(for) p 3301 4057 a(a.e.) p Fn 448 4182 a(!) p Fp 508 4182 a(,) p 572 4182 a(whic) m(h) p 839 4182 a(implies) p 1154 4182 a(\() p Fn(A\016) p Fl 1297 4196 a(0) p Fp 1337 4182 a(\)\() p Fn(x) p Fp(\)) p 1532 4182 a(=) p Fn 1639 4182 a(A) p Fp(\() p Fn(!) p Fp 1817 4182 a(;) p Fn 1857 4182 a(x;) p Fp 1949 4182 a(0\)) p Fh 2067 4182 a(2) p Fn 2164 4182 a(l) p Fl 2193 4149 a(2) p Fp 2232 4182 a(\() p Fk(Z) p 2287 4182 a(Z) p Fj 2342 4145 a(d) p Fp 2383 4182 a(\)) p 2455 4182 a(w.r.t.) p Fn 2728 4182 a(x) p Fp 2817 4182 a(for) p 2962 4182 a(a.e.) p Fn 3159 4182 a(!) p Fp 3219 4182 a(.) p 3304 4182 a(F) p 3355 4182 a(or) 448 4306 y(suc) m(h) p Fn 653 4306 a(!) p Fh 738 4306 a(2) p Fp 824 4306 a(\012,) p 946 4306 a(\() p Fn(B) p 1055 4306 a(A) p Fp(\)\() p Fn(!) p Fp 1268 4306 a(;) p Fn 1308 4306 a(x;) p Fp 1400 4306 a(0\)) p 1507 4306 a(=) p 1603 4306 a(\() p Fn(B) p 1712 4306 a(A\016) p Fl 1820 4320 a(0) p Fp 1860 4306 a(\)\() p Fn(x) p Fp(\)) p Fh 2043 4306 a(2) p Fn 2129 4306 a(l) p Fl 2158 4273 a(2) p Fp 2197 4306 a(\() p Fk(Z) p 2252 4306 a(Z) p Fj 2308 4269 a(d) p Fp 2348 4306 a(\),) p 2439 4306 a(and) p Fi 978 4392 a(X) p Fj 947 4591 a(x) p Fm(2) p Fg(Z) p 1050 4591 a(Z) p Ff 1093 4565 a(d) p Fh 1144 4473 a(j) p Fn(B) p 1243 4473 a(A) p Fp(\() p Fn(!) p Fp 1422 4473 a(;) p Fn 1462 4473 a(x;) p Fp 1554 4473 a(0\)) p Fh(j) p Fl 1659 4436 a(2) p Fp 1725 4473 a(=) p Fh 1821 4473 a(k) p Fp(\() p Fn(B) p 1975 4473 a(A\016) p Fl 2083 4487 a(0) p Fp 2123 4473 a(\)\() p Fn(x) p Fp(\)) p Fh(k) p Fl 2325 4436 a(2) p Fj 2325 4509 a(l) p Fc 2347 4490 a(2) p Fl 2383 4509 a(\() p Fg(Z) p 2426 4509 a(Z) p Ff 2470 4483 a(d) p Fl 2506 4509 a(\)) p Fp 448 4473 a(\(2.12\)) p Fh 1725 4717 a(\024) p 1821 4717 a(k) p Fn(B) p Fh 1940 4717 a(k) p Fl 1985 4679 a(2) p Fj 1985 4739 a(op) p Fh 2059 4717 a(k) p Fp(\() p Fn(A\016) p Fl 2247 4731 a(0) p Fp 2288 4717 a(\)\() p Fn(x) p Fp(\)) p Fh(k) p Fl 2490 4679 a(2) p Fj 2490 4753 a(l) p Fc 2512 4734 a(2) p Fl 2548 4753 a(\() p Fg(Z) p 2591 4753 a(Z) p Ff 2634 4727 a(d) p Fl 2671 4753 a(\)) p Fh 1725 4892 a(\024) p Fp 1825 4892 a(sup) p Fj 1821 4969 a(!) p Fm 1867 4969 a(2) p Fl(\012) p Fh 1980 4892 a(k) p Fn(B) p Fh 2099 4892 a(k) p Fl 2144 4854 a(2) p Fj 2144 4914 a(op) p Fi 2265 4811 a(X) p Fj 2234 5010 a(x) p Fm(2) p Fg(Z) p 2337 5010 a(Z) p Ff 2380 4984 a(d) p Fh 2431 4892 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2635 4892 a(;) p Fn 2675 4892 a(x;) p Fp 2767 4892 a(0\)) p Fh(j) p Fl 2872 4854 a(2) p Fn 2913 4892 a(:) p Fp 1897 5225 a(13) p eop %%Page: 14 14 14 13 bop 448 573 a @beginspecial @setspecial @endspecial Fp(In) p 570 573 a(\(2.12\),) p 868 573 a(w) m(e) p 1009 573 a(recall) p 1260 573 a(that) p Fn 1465 573 a(B) p Fp 1577 573 a(=) p Fh 1686 573 a(f) p Fn(B) p Fj 1800 587 a(!) p Fh 1851 573 a(g) p Fj 1896 587 a(!) p Fm 1942 587 a(2) p Fl(\012) p Fp 2045 573 a(,) p 2110 573 a(where) p Fn 2381 573 a(B) p Fj 2450 587 a(!) p Fp 2539 573 a(is) p 2638 573 a(a) p 2722 573 a(b) s(ounded) p 3101 573 a(op) s(erator) 448 697 y(on) p Fn 580 697 a(l) p Fl 609 664 a(2) p Fp 649 697 a(\() p Fk(Z) p 704 697 a(Z) p Fj 759 661 a(d) p Fp 799 697 a(\)) p 870 697 a(for) p 1015 697 a(an) m(y) p 1192 697 a(\014xed) p Fn 1418 697 a(!) p Fh 1512 697 a(2) p Fp 1607 697 a(\012.) p 1755 697 a(Since) p 1998 697 a(the) p 2160 697 a(RHS) p 2382 697 a(of) p 2491 697 a(\(2.12\)) p Fh(2) p Fn 2818 697 a(L) p Fl 2880 664 a(1) p Fp 2920 697 a(\(\012\),) p 3118 697 a(w) m(e) p 3258 697 a(ha) m(v) m(e) p Fn 448 822 a(B) p 522 822 a(A) p Fh 627 822 a(2) p 724 822 a(L) p Fl 787 789 a(2) p Fp 826 822 a(,) p 890 822 a(and) p Fh 1073 822 a(k) p Fn(B) p 1192 822 a(A) p Fh(k) p Fm 1305 842 a(L) p Fc 1354 823 a(2) p Fh 1430 822 a(\024) p Fp 1537 822 a(sup) p Fj 1674 844 a(!) p Fm 1720 844 a(2) p Fl(\012) p Fh 1837 822 a(k) p Fn(B) p Fh 1956 822 a(k) p Fj 2001 836 a(op) p Fh 2075 822 a(k) p Fn(A) p Fh(k) p Fm 2233 842 a(L) p Fc 2282 823 a(2) p Fp 2322 822 a(.) p 2408 822 a(By) p 2557 822 a(Lemma) p 2888 822 a(2.2,) p Fn 3069 822 a(A) p Fm 3137 789 a(\003) p Fh 3213 822 a(2) p 3310 822 a(L) p Fl 3373 789 a(2) p Fp 3412 822 a(,) 448 946 y(and) p Fh 623 946 a(k) p Fn(A) p Fm 736 913 a(\003) p Fh 776 946 a(k) p Fm 821 966 a(L) p Fc 870 947 a(2) p Fp 934 946 a(=) p 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1857 1163 a(\003) p Fp 1897 1196 a(\() p Fn(!) p Fp 2007 1196 a(;) p Fn 2047 1196 a(x;) p 2139 1196 a(y) p Fp 2187 1196 a(\)) p 2254 1196 a(=) p Fn 2355 1196 a(B) p Fm 2429 1163 a(\003) p Fn 2468 1196 a(A) p Fm 2536 1163 a(\003) p Fp 2576 1196 a(\() p Fn(!) p Fp 2686 1196 a(;) p Fn 2726 1196 a(x;) p 2818 1196 a(y) p Fp 2866 1196 a(\)) p Fn(;) p Fp 2961 1196 a(as) p 3075 1196 a(functions) 448 1320 y(on) p 584 1320 a(\012) p Fh 676 1320 a(\002) p Fk 773 1320 a(Z) p 793 1320 a(Z) p Fj 848 1283 a(d) p Fh 914 1320 a(\002) p Fk 1012 1320 a(Z) p 1032 1320 a(Z) p Fj 1086 1283 a(d) p Fp 1127 1320 a(.) p 1220 1320 a(By) p 1372 1320 a(what) p 1609 1320 a(w) m(e) p 1752 1320 a(ha) m(v) m(e) p 1970 1320 a(just) p 2159 1320 a(sho) m(wn,) p Fn 2472 1320 a(B) p Fm 2546 1287 a(\003) p Fn 2585 1320 a(A) p Fm 2653 1287 a(\003) p Fh 2733 1320 a(2) p 2835 1320 a(L) p Fl 2898 1287 a(2) p Fp 2937 1320 a(.) p 3030 1320 a(Therefore,) 448 1445 y(\() p Fn(AB) p Fp 625 1445 a(\)) p Fm 660 1412 a(\003) p Fp 700 1445 a(,) p 757 1445 a(and) p 935 1445 a(hence,) p Fn 1214 1445 a(AB) p Fh 1383 1445 a(2) p 1470 1445 a(L) p Fl 1533 1412 a(2) p Fp 1572 1445 a(.) p 1641 1445 a(Since) p Fh 1880 1445 a(k) p Fn(B) p Fh 1999 1445 a(k) p Fj 2044 1459 a(op) p Fp 2145 1445 a(=) p Fh 2243 1445 a(k) p Fn(B) p Fm 2362 1412 a(\003) p Fh 2401 1445 a(k) p Fj 2446 1459 a(op) p Fp 2520 1445 a(,) p 2577 1445 a(and) p Fh 2755 1445 a(k) p Fn(A) p Fh(k) p Fm 2913 1464 a(L) p Fc 2962 1445 a(2) p Fp 3028 1445 a(=) p Fh 3126 1445 a(k) p Fn(A) p Fm 3239 1412 a(\003) p Fh 3279 1445 a(k) p Fm 3324 1464 a(L) p Fc 3373 1445 a(2) p Fp 3412 1445 a(,) 448 1569 y(w) m(e) p 582 1569 a(ha) m(v) m(e) p Fh 1361 1735 a(k) p Fn(AB) p Fh 1548 1735 a(k) p Fm 1593 1755 a(L) p Fc 1642 1736 a(2) p Fp 1706 1735 a(=) p Fh 1802 1735 a(k) p Fp(\() p Fn(AB) p Fp 2024 1735 a(\)) p Fm 2059 1698 a(\003) p Fh 2099 1735 a(k) p Fm 2144 1755 a(L) p Fc 2193 1736 a(2) p Fp 1706 1885 a(=) p Fh 1802 1885 a(k) p Fn(B) p Fm 1921 1847 a(\003) p Fn 1960 1885 a(A) p Fm 2028 1847 a(\003) p Fh 2068 1885 a(k) p Fm 2113 1905 a(L) p Fc 2162 1886 a(2) p Fh 1706 2034 a(\024) p Fp 1806 2034 a(sup) p Fj 1802 2111 a(!) p Fm 1848 2111 a(2) p Fl(\012) p Fh 1961 2034 a(k) p Fn(B) p Fm 2080 1997 a(\003) p Fh 2120 2034 a(k) p Fj 2165 2048 a(op) p Fh 2239 2034 a(k) p Fn(A) p Fm 2352 1997 a(\003) p Fh 2392 2034 a(k) p Fm 2437 2054 a(L) p Fc 2486 2035 a(2) p Fp 1706 2225 a(=) p 1806 2225 a(sup) p Fj 1802 2302 a(!) p Fm 1848 2302 a(2) p Fl(\012) p Fh 1961 2225 a(k) p Fn(B) p Fh 2080 2225 a(k) p Fj 2125 2239 a(op) p Fh 2199 2225 a(k) p Fn(A) p Fh(k) p Fm 2357 2245 a(L) p Fc 2406 2226 a(2) p Fn 2446 2225 a(:) 589 2557 y @beginspecial @setspecial @endspecial Fp(T) p 647 2557 a(o) p 721 2557 a(pro) m(v) m(e) p 964 2557 a(\(2\)) p 1108 2557 a(of) p 1209 2557 a(Prop) s(osition) p 1696 2557 a(2.5,) p 1866 2557 a(w) m(e) p 1997 2557 a(prepare) p 2324 2557 a(the) p 2478 2557 a(follo) m(wing) p 2859 2557 a(Lemma,) p 3207 2557 a(whic) m(h) 448 2682 y(is) p 540 2682 a(not) p Fo 701 2682 a(a) p 780 2682 a(priori) p Fp 1036 2682 a(trivial.) p Fe 448 2840 a(Lemma) p 819 2840 a(2.3) p 998 2840 a @beginspecial @setspecial @endspecial Fo(L) p 1050 2840 a(et) p Fn 1146 2840 a(A) p Fo(,) p Fn 1268 2840 a(C) p Fh 1364 2840 a(2) p 1450 2840 a(L) p Fl 1513 2807 a(2) p Fo 1552 2840 a(,) p 1606 2840 a(and) p Fn 1773 2840 a(B) p Fh 1872 2840 a(2) p 1958 2840 a(A) p Fo(.) p 2097 2840 a(Then,) p 2355 2840 a(as) p 2462 2840 a(functions) p 2848 2840 a(on) p Fp 2970 2840 a(\012) p Fh 3037 2840 a(\002) p Fk 3109 2840 a(Z) p 3128 2840 a(Z) p Fj 3182 2803 a(d) p Fh 3223 2840 a(\002) p Fk 3295 2840 a(Z) p 3314 2840 a(Z) p Fj 3369 2803 a(d) p Fo 3409 2840 a(,) p Fi 971 2912 a(\020) p Fp 1020 3006 a(\() p Fn(AB) p Fp 1197 3006 a(\)) p Fn(C) p Fi 1304 2912 a(\021) p Fp 1354 3006 a(\() p Fn(!) p Fp 1464 3006 a(;) p Fn 1504 3006 a(x;) p 1596 3006 a(y) p Fp 1644 3006 a(\)) p 1705 3006 a(=) p Fi 1801 2912 a(\020) p Fn 1851 3006 a(A) p Fp(\() p Fn(B) p 2028 3006 a(C) p Fp 2100 3006 a(\)) p Fi 2135 2912 a(\021) p Fp 2184 3006 a(\() p Fn(!) p Fp 2295 3006 a(;) p Fn 2335 3006 a(x;) p 2427 3006 a(y) p Fp 2475 3006 a(\)) p Fn(;) p Fo 2644 3006 a(a.e.) p Fn 2830 3006 a(!) s(:) 448 3421 y @beginspecial @setspecial @endspecial Fo(Pr) p 543 3421 a(o) p 584 3421 a(of.) p Fp 773 3421 a(By) p 931 3421 a(Prop) s(osition) p 1435 3421 a(2.3,) p 1626 3421 a(w) m(e) p 1775 3421 a(can) p 1956 3421 a(tak) m(e) p 2168 3421 a(sequence) p 2560 3421 a(of) p 2679 3421 a(b) s(ounded) p 3065 3421 a(op) s(erators) p Fh 448 3546 a(f) p Fn(A) p Fj 561 3560 a(n) p Fh 609 3546 a(g) p Fm 654 3513 a(1) p Fj 654 3569 a(n) p Fl(=1) p Fp 792 3546 a(,) p Fh 852 3546 a(f) p Fn(C) p Fj 962 3560 a(n) p Fh 1009 3546 a(g) p Fm 1054 3513 a(1) p Fj 1054 3569 a(n) p Fl(=1) p Fh 1223 3546 a(\032) p 1325 3546 a(A) p Fp 1432 3546 a(whic) m(h) p 1696 3546 a(satisfy) p Fn 1983 3546 a(A) p Fj 2051 3560 a(n) p Fh 2130 3546 a(!) p Fn 2252 3546 a(A) p Fp(,) p Fn 2380 3546 a(C) p Fj 2445 3560 a(n) p Fh 2524 3546 a(!) p Fn 2646 3546 a(C) p Fp 2751 3546 a(in) p Fh 2861 3546 a(L) p Fl 2924 3513 a(2) p Fp 2997 3546 a(as) p Fn 3113 3546 a(n) p Fh 3199 3546 a(!) p 3321 3546 a(1) p Fp(.) 448 3670 y(Then,) p 715 3670 a(b) m(y) p 845 3670 a(Prop) s(osition) p 1338 3670 a(2.5) p 1488 3670 a(\(1\),) p Fn 1665 3670 a(A) p Fj 1733 3684 a(n) p Fn 1780 3670 a(B) p Fh 1884 3670 a(!) p Fn 2007 3670 a(AB) p Fp 2149 3670 a(,) p Fn 2208 3670 a(B) p 2282 3670 a(C) p Fj 2347 3684 a(n) p Fh 2425 3670 a(!) p Fn 2547 3670 a(B) p 2621 3670 a(C) p Fp 2693 3670 a(,) p 2752 3670 a(in) p Fh 2862 3670 a(L) p Fl 2925 3637 a(2) p Fp 2998 3670 a(as) p Fn 3113 3670 a(n) p Fh 3199 3670 a(!) p 3321 3670 a(1) p Fp(.) 448 3795 y(Moreo) m(v) m (er,) p 873 3795 a(b) m(y) p 999 3795 a(Sc) m(h) m(w) m(arz) p 1351 3795 a(inequalit) m(y) p 1772 3795 a(and) p 1949 3795 a(\(2.6\),) p Fi 598 3868 a(Z) p Fl 644 4056 a(\012) p Fn 714 3983 a(d) p Fe(P) p Fi 832 3885 a(\014) 832 3935 y(\014) 832 3985 y(\014) 861 3889 y(\020) p Fp 910 3983 a(\() p Fn(AB) p Fp 1087 3983 a(\)) p Fn(C) p Fi 1194 3889 a(\021) p Fp 1244 3983 a(\() p Fn(!) p Fp 1354 3983 a(;) p Fn 1394 3983 a(x;) p 1486 3983 a(y) p Fp 1534 3983 a(\)) p Fi 1569 3885 a(\014) 1569 3935 y(\014) 1569 3985 y(\014) p Fh 1623 3983 a(\024) p Fi 1719 3868 a(Z) p Fl 1765 4056 a(\012) p Fn 1835 3983 a(d) p Fe(P) p Fi 1998 3902 a(X) p Fj 1969 4100 a(z) p Fm 2005 4100 a(2) p Fg(Z) p 2068 4100 a(Z) p Ff 2111 4075 a(d) p Fh 2162 3983 a(j) p Fp(\() p Fn(AB) p Fp 2364 3983 a(\)\() p Fn(!) p Fp 2510 3983 a(;) p Fn 2550 3983 a(x;) p 2642 3983 a(z) p Fp 2688 3983 a(\)) p Fh(jj) p Fn(C) p Fp 2845 3983 a(\() p Fn(!) p Fp 2957 3983 a(;) p Fn 2997 3983 a(z) t(;) p 3083 3983 a(y) p Fp 3131 3983 a(\)) p Fh(j) 1623 4267 y(\024) p Fi 1719 4173 a(\020) 1768 4152 y(Z) p Fl 1815 4341 a(\012) p Fn 1885 4267 a(d) p Fe(P) p Fi 2048 4186 a(X) p Fj 2019 4385 a(z) p Fm 2055 4385 a(2) p Fg(Z) p 2118 4385 a(Z) p Ff 2160 4359 a(d) p Fh 2212 4267 a(j) p Fp(\() p Fn(AB) p Fp 2414 4267 a(\)\() p Fn(!) p Fp 2560 4267 a(;) p Fn 2600 4267 a(x;) p 2692 4267 a(z) p Fp 2738 4267 a(\)) p Fh(j) p Fl 2798 4230 a(2) p Fi 2839 4173 a(\021) p Fl 2888 4196 a(1) p Fj(=) p Fl(2) p Fh 3019 4267 a(\002) 2082 4552 y(\002) p Fi 2153 4457 a(\020) 2203 4437 y(Z) p Fl 2249 4625 a(\012) p Fn 2319 4552 a(d) p Fe(P) p Fi 2482 4471 a(X) p Fj 2453 4669 a(z) p Fm 2489 4669 a(2) p Fg(Z) p 2552 4669 a(Z) p Ff 2595 4644 a(d) p Fh 2646 4552 a(j) p Fn(C) p Fp 2743 4552 a(\() p Fn(!) p Fp 2853 4552 a(;) p Fn 2893 4552 a(z) t(;) p 2979 4552 a(y) p Fp 3027 4552 a(\)) p Fh(j) p Fl 3087 4514 a(2) p Fi 3128 4457 a(\021) p Fl 3178 4480 a(1) p Fj(=) p Fl(2) p Fp 1623 4783 a(=) p Fh 1719 4783 a(k) p Fn(AB) p Fh 1906 4783 a(k) p Fm 1951 4803 a(L) p Fc 2000 4784 a(2) p Fh 2039 4783 a(k) p Fn(C) p Fh 2156 4783 a(k) p Fm 2201 4803 a(L) p Fc 2250 4784 a(2) p Fh 1623 4933 a(\024) p Fp 1723 4933 a(sup) p Fj 1719 5010 a(!) p Fm 1765 5010 a(2) p Fl(\012) p Fh 1878 4933 a(k) p Fn(B) p Fh 1997 4933 a(k) p Fj 2042 4947 a(op) p Fh 2116 4933 a(k) p Fn(A) p Fh(k) p Fm 2274 4952 a(L) p Fc 2323 4933 a(2) p Fh 2363 4933 a(k) p Fn(C) p Fh 2480 4933 a(k) p Fm 2525 4952 a(L) p Fc 2574 4933 a(2) p Fn 2612 4933 a(:) p Fp 1897 5225 a(14) p eop %%Page: 15 15 15 14 bop 448 573 a @beginspecial @setspecial @endspecial Fp(Therefore,) p 886 573 a(for) p 1025 573 a(an) m(y) p 1197 573 a(\014xed) p 1416 573 a(\() p Fn(x;) p 1543 573 a(y) p Fp 1591 573 a(\)) p Fh 1652 573 a(2) p Fk 1738 573 a(Z) p 1758 573 a(Z) p Fj 1813 536 a(d) p Fh 1874 573 a(\002) p Fk 1965 573 a(Z) p 1985 573 a(Z) p Fj 2039 536 a(d) p Fp 2080 573 a(,) p Fi 1106 695 a(\020) p Fp 1156 789 a(\() p Fn(A) p Fj 1259 803 a(n) p Fn 1306 789 a(B) p Fp 1380 789 a(\)) p Fn(C) p Fj 1480 803 a(n) p Fi 1527 695 a(\021) p Fp 1577 789 a(\() p Fn(!) p Fp 1687 789 a(;) p Fn 1727 789 a(x;) p 1819 789 a(y) p Fp 1867 789 a(\)) p Fh 1928 789 a(!) p Fi 2045 695 a(\020) p Fp 2094 789 a(\() p Fn(AB) p Fp 2271 789 a(\)) p Fn(C) p Fi 2378 695 a(\021) p Fp 2428 789 a(\() p Fn(!) p Fp 2538 789 a(;) p Fn 2578 789 a(x;) p 2670 789 a(y) p Fp 2718 789 a(\)) p Fn(;) 448 1023 y @beginspecial @setspecial @endspecial Fp(as) p Fn 561 1023 a(n) p Fh 642 1023 a(!) p 759 1023 a(1) p Fp 881 1023 a(in) p Fn 988 1023 a(L) p Fl 1050 990 a(1) p Fp 1090 1023 a(\(\012\).) p 1294 1023 a(Since) p Fk 1532 1023 a(Z) p 1552 1023 a(Z) p Fj 1607 986 a(d) p Fh 1668 1023 a(\002) p Fk 1760 1023 a(Z) p 1780 1023 a(Z) p Fj 1834 986 a(d) p Fp 1906 1023 a(is) p 1998 1023 a(coun) m(table,) p 2436 1023 a(b) m(y) p 2563 1023 a(diagonal) p 2927 1023 a(tric) m(k,) p 3166 1023 a(w) m(e) p 3301 1023 a(can) 448 1148 y(tak) m(e) p 645 1148 a(a) p 721 1148 a(subsequence) p Fn 1235 1148 a(n) p Fm 1290 1115 a(0) p Fp 1338 1148 a(=) p Fn 1434 1148 a(n) p Fm 1489 1115 a(0) p Fp 1512 1148 a(\() p Fn(k) p Fp 1597 1148 a(\)) p 1663 1148 a(suc) m(h) p 1868 1148 a(that) p Fi 1106 1270 a(\020) p Fp 1156 1364 a(\() p Fn(A) p Fj 1259 1378 a(n) p Fn 1306 1364 a(B) p Fp 1380 1364 a(\)) p Fn(C) p Fj 1480 1378 a(n) p Fi 1527 1270 a(\021) p Fp 1577 1364 a(\() p Fn(!) p Fp 1687 1364 a(;) p Fn 1727 1364 a(x;) p 1819 1364 a(y) p Fp 1867 1364 a(\)) p Fh 1928 1364 a(!) p Fi 2045 1270 a(\020) p Fp 2094 1364 a(\() p Fn(AB) p Fp 2271 1364 a(\)) p Fn(C) p Fi 2378 1270 a(\021) p Fp 2428 1364 a(\() p Fn(!) p Fp 2538 1364 a(;) p Fn 2578 1364 a(x;) p 2670 1364 a(y) p Fp 2718 1364 a(\)) p Fn(;) 448 1598 y @beginspecial @setspecial @endspecial Fp(p) s(oin) m(t) m(wise) p 854 1598 a(for) p 997 1598 a(a.e.) p Fn 1185 1598 a(!) p Fp 1245 1598 a(,) p 1305 1598 a(as) p Fn 1420 1598 a(k) p Fh 1502 1598 a(!) p 1624 1598 a(1) p Fp(,) p 1775 1598 a(for) p 1918 1598 a(an) m(y) p Fn 2093 1598 a(x) p Fp(,) p Fn 2206 1598 a(y) p Fh 2285 1598 a(2) p Fk 2377 1598 a(Z) p 2397 1598 a(Z) p Fj 2452 1561 a(d) p Fp 2492 1598 a(.) p 2569 1598 a(Similarly) p 2921 1598 a(,) p 2978 1598 a(b) m(y) p 3108 1598 a(taking) p 3392 1598 a(a) 448 1723 y(subsequence) p 962 1723 a(further:) p Fn 1303 1723 a(n) p Fm 1358 1690 a(00) p Fp 1426 1723 a(=) p Fn 1522 1723 a(n) p Fm 1577 1690 a(00) p Fp 1619 1723 a(\() p Fn(n) p Fm 1709 1690 a(0) p Fp 1732 1723 a(\() p Fn(k) p Fp 1817 1723 a(\)\),) p Fi 1106 1845 a(\020) p Fn 1156 1939 a(A) p Fj 1224 1953 a(n) p Fp 1271 1939 a(\() p Fn(B) p 1380 1939 a(C) p Fj 1445 1953 a(n) p Fp 1492 1939 a(\)) p Fi 1527 1845 a(\021) p Fp 1577 1939 a(\() p Fn(!) p Fp 1687 1939 a(;) p Fn 1727 1939 a(x;) p 1819 1939 a(y) p Fp 1867 1939 a(\)) p Fh 1928 1939 a(!) p Fi 2045 1845 a(\020) p Fn 2094 1939 a(A) p Fp(\() p Fn(B) p 2271 1939 a(C) p Fp 2343 1939 a(\)) p Fi 2378 1845 a(\021) p Fp 2428 1939 a(\() p Fn(!) p Fp 2538 1939 a(;) p Fn 2578 1939 a(x;) p 2670 1939 a(y) p Fp 2718 1939 a(\)) p Fn(;) 448 2155 y @beginspecial @setspecial @endspecial Fp(p) s(oin) m(t) m(wise) p 850 2155 a(for) p 989 2155 a(a.e.) p Fn 1166 2155 a(!) p Fp 1226 2155 a(,) p 1282 2155 a(as) p Fn 1393 2155 a(k) p Fh 1469 2155 a(!) p 1585 2155 a(1) p Fp(.) p 1741 2155 a(Therefore,) p 2179 2155 a(it) p 2270 2155 a(is) p 2361 2155 a(su\016cien) m(t) p 2743 2155 a(to) p 2854 2155 a(sho) m(w) p Fi 1073 2276 a(\020) p Fp 1122 2370 a(\() p Fn(A) p Fj 1225 2384 a(n) p Fn 1273 2370 a(B) p Fp 1347 2370 a(\)) p Fn(C) p Fj 1447 2384 a(n) p Fi 1494 2276 a(\021) p Fp 1543 2370 a(\() p Fn(!) p Fp 1654 2370 a(;) p Fn 1694 2370 a(x;) p 1786 2370 a(y) p Fp 1834 2370 a(\)) p 1895 2370 a(=) p Fi 1991 2276 a(\020) p Fn 2040 2370 a(A) p Fj 2108 2384 a(n) p Fp 2155 2370 a(\() p Fn(B) p 2264 2370 a(C) p Fj 2329 2384 a(n) p Fp 2376 2370 a(\)) p Fi 2411 2276 a(\021) p Fp 2461 2370 a(\() p Fn(!) p Fp 2572 2370 a(;) p Fn 2612 2370 a(x;) p 2704 2370 a(y) p Fp 2752 2370 a(\)) p Fn(;) 448 2605 y @beginspecial @setspecial @endspecial Fp(p) s(oin) m(t) m(wise,) p 876 2605 a(whic) m(h) p 1136 2605 a(is) p 1227 2605 a(clear.) p 1480 2605 a(In) p 1594 2605 a(fact,) p 1798 2605 a(since) p Fn 2021 2605 a(A) p Fj 2089 2619 a(n) p Fp 2136 2605 a(,) p Fn 2192 2605 a(B) p Fp 2266 2605 a(,) p Fn 2321 2605 a(C) p Fj 2386 2619 a(n) p Fp 2463 2605 a(are) p 2615 2605 a(b) s(ounded) p 2986 2605 a(on) p Fn 3112 2605 a(l) p Fl 3141 2572 a(2) p Fp 3180 2605 a(\() p Fk(Z) p 3235 2605 a(Z) p Fj 3291 2568 a(d) p Fp 3331 2605 a(\),) p Fi 1016 2727 a(\020) p Fp 1066 2821 a(\() p Fn(A) p Fj 1169 2835 a(n) p Fn 1216 2821 a(B) p Fp 1290 2821 a(\)) p Fn(C) p Fj 1390 2835 a(n) p Fi 1437 2727 a(\021) p Fp 1487 2821 a(\() p Fn(!) p Fp 1597 2821 a(;) p Fn 1637 2821 a(x;) p 1729 2821 a(y) p Fp 1777 2821 a(\)) p 1838 2821 a(=) p Fn 1934 2821 a(<) p 2030 2821 a(\016) p Fj 2070 2835 a(x) p Fn 2115 2821 a(;) p 2155 2821 a(A) p Fj 2223 2835 a(n) p Fn 2270 2821 a(B) p 2344 2821 a(C) p Fj 2409 2835 a(n) p Fn 2456 2821 a(\016) p Fj 2496 2835 a(y) p Fn 2563 2821 a(>) p Fj 2634 2850 a(l) p Fc 2656 2831 a(2) p Fl 2690 2850 a(\() p Fg(Z) p 2733 2850 a(Z) p Ff 2776 2824 a(d) p Fl 2812 2850 a(\)) p Fp 1838 3003 a(=) p Fi 1934 2909 a(\020) p Fn 1984 3003 a(A) p Fj 2052 3017 a(n) p Fp 2099 3003 a(\() p Fn(B) p 2208 3003 a(C) p Fj 2273 3017 a(n) p Fp 2320 3003 a(\)) p Fi 2355 2909 a(\021) p Fp 2405 3003 a(\() p Fn(!) p Fp 2515 3003 a(;) p Fn 2555 3003 a(x;) p 2647 3003 a(y) p Fp 2695 3003 a(\)) p Fn(:) p 448 3155 60 4 v 448 3244 4 89 v 504 3244 V 448 3247 60 4 v 448 3468 a @beginspecial @setspecial @endspecial Fo(Pr) p 543 3468 a(o) p 584 3468 a(of) p 692 3468 a(of) p 799 3468 a(Pr) p 894 3468 a(op) p 981 3468 a(osition) p 1283 3468 a(2.5) p 1436 3468 a(\(2\)) 589 3593 y @beginspecial @setspecial @endspecial Fp(Let) p Fn 752 3593 a(A) p Fp(,) p Fn 876 3593 a(C) p Fh 973 3593 a(2) p 1059 3593 a(L) p Fl 1122 3560 a(2) p Fp 1161 3593 a(,) p 1216 3593 a(and) p Fn 1393 3593 a(B) p Fh 1492 3593 a(2) p 1578 3593 a(A) p Fp(.) p 1716 3593 a(By) p 1859 3593 a(Prop) s(osition) p 2348 3593 a(2.4,) p Fn 1350 3809 a(<) p 1446 3809 a(B) p 1520 3809 a(A;) p 1628 3809 a(C) p 1725 3809 a(>) p Fm 1796 3828 a(L) p Fc 1845 3810 a(2) p Fp 1908 3809 a(=) p Fh 2004 3809 a(T) p Fp 2077 3809 a(\(\() p Fn(B) p 2221 3809 a(A) p Fp(\)) p Fm 2324 3771 a(\003) p Fn 2364 3809 a(C) p Fp 2436 3809 a(\)) 1908 3958 y(=) p Fh 2004 3958 a(T) p Fp 2077 3958 a(\(\() p Fn(A) p Fm 2215 3921 a(\003) p Fn 2255 3958 a(B) p Fm 2329 3921 a(\003) p Fp 2368 3958 a(\)) p Fn(C) p Fp 2475 3958 a(\)) p Fn(:) 448 4174 y @beginspecial @setspecial @endspecial Fp(By) p 591 4174 a(Prop) s(osition) p 1080 4174 a(2.2,) p 1252 4174 a(and) p 1429 4174 a(Lemma) p 1753 4174 a(2.3,) p Fh 1122 4406 a(T) p Fp 1194 4406 a(\(\() p Fn(A) p Fm 1332 4369 a(\003) p Fn 1373 4406 a(B) p Fm 1447 4369 a(\003) p Fp 1486 4406 a(\)) p Fn(C) p Fp 1593 4406 a(\)) p 1653 4406 a(=) p Fi 1749 4291 a(Z) p Fl 1795 4480 a(\012) p Fn 1865 4406 a(d) p Fe(P) p Fi 1983 4312 a(\020) p Fp 2034 4406 a(\() p Fn(A) p Fm 2137 4369 a(\003) p Fn 2177 4406 a(B) p Fm 2251 4369 a(\003) p Fp 2290 4406 a(\)) p Fn(C) p Fi 2397 4312 a(\021) p Fp 2446 4406 a(\() p Fn(!) p Fp 2557 4406 a(;) p 2597 4406 a(0) p Fn(;) p Fp 2682 4406 a(0\)) 1653 4628 y(=) p Fi 1749 4513 a(Z) p Fl 1795 4702 a(\012) p Fn 1865 4628 a(d) p Fe(P) p Fi 1983 4534 a(\020) p Fn 2034 4628 a(A) p Fm 2102 4591 a(\003) p Fp 2141 4628 a(\() p Fn(B) p Fm 2250 4591 a(\003) p Fn 2290 4628 a(C) p Fp 2362 4628 a(\)) p Fi 2397 4534 a(\021) p Fp 2446 4628 a(\() p Fn(!) p Fp 2557 4628 a(;) p 2597 4628 a(0) p Fn(;) p Fp 2682 4628 a(0\)) 1653 4804 y(=) p Fh 1749 4804 a(T) p Fp 1822 4804 a(\() p Fn(A) p Fm 1925 4766 a(\003) p Fp 1965 4804 a(\() p Fn(B) p Fm 2074 4766 a(\003) p Fn 2113 4804 a(C) p Fp 2185 4804 a(\)\)) 1653 4953 y(=) p Fn 1749 4953 a(<) p 1845 4953 a(A;) p 1953 4953 a(B) p Fm 2027 4915 a(\003) p Fn 2067 4953 a(C) p 2163 4953 a(>) p Fm 2234 4973 a(L) p Fc 2283 4954 a(2) p Fn 2347 4953 a(:) p Fp 1897 5225 a(15) p eop %%Page: 16 16 16 15 bop 448 573 a @beginspecial @setspecial @endspecial Fp(Therefore,) p 884 573 a(the) p 1039 573 a(adjoin) m(t) p 1345 573 a(of) p 1447 573 a(the) p 1602 573 a(linear) p 1852 573 a(b) s(ounded) p 2222 573 a(op) s(erator) p Fn 2587 573 a(A) p Fh 2680 573 a(7!) p Fn 2796 573 a(B) p 2870 573 a(A) p Fp 2966 573 a(on) p Fh 3091 573 a(L) p Fl 3154 540 a(2) p Fp 3221 573 a(is) p 3311 573 a(the) 448 697 y(map) p Fn 651 697 a(A) p Fh 746 697 a(7!) p Fn 864 697 a(B) p Fm 938 664 a(\003) p Fn 976 697 a(A) p Fp(.) p 1113 697 a(The) p 1300 697 a(adjoin) m(t) p 1609 697 a(op) s(erator) p 1977 697 a(of) p Fn 2081 697 a(A) p Fh 2176 697 a(7!) p Fn 2294 697 a(AB) p Fp 2466 697 a(can) p 2634 697 a(b) s(e) p 2759 697 a(deriv) m(ed) p 3078 697 a(similarly) p 3415 697 a(.) p 448 758 60 4 v 448 847 4 89 v 504 847 V 448 850 60 4 v 589 946 a @beginspecial @setspecial @endspecial(W) p 674 946 a(e) p 745 946 a(are) p 897 946 a(going) p 1138 946 a(to) p 1249 946 a(study) p 1499 946 a(un) m(b) s(ounded) p 1968 946 a(op) s(erators) p 2370 946 a(on) p Fh 2495 946 a(L) p Fl 2558 913 a(2) p Fp 2597 946 a(.) p 2663 946 a(The) p 2849 946 a(follo) m(wing) p 3232 946 a(op) s(er-) 448 1071 y(ator) p 640 1071 a(corresp) s(onds) p 1139 1071 a(to) p 1251 1071 a(taking) p 1531 1071 a(comm) m(utator) p 2044 1071 a(with) p Fn 2251 1071 a(x) p Fl 2303 1085 a(1) p Fp 2342 1071 a(.) p Fe 448 1270 a(Prop) s(osition) p 1014 1270 a(2.6) p 1193 1270 a @beginspecial @setspecial @endspecial Fo(F) p 1245 1270 a(or) p Fn 1362 1270 a(A) p Fh 1456 1270 a(2) p 1542 1270 a(L) p Fl 1605 1237 a(2) p Fo 1644 1270 a(,) p 1704 1270 a(we) p 1839 1270 a(de\014ne) p Fp 1205 1486 a(\() p Fn(@) p Fl 1288 1500 a(1) p Fn 1328 1486 a(A) p Fp(\)\() p Fn(!) p Fp 1542 1486 a(;) p Fn 1582 1486 a(x;) p 1674 1486 a(y) p Fp 1722 1486 a(\)) p 1783 1486 a(:=) p 1904 1486 a(\() p Fn(x) p Fl 1991 1500 a(1) p Fh 2051 1486 a(\000) p Fn 2142 1486 a(y) p Fl 2187 1500 a(1) p Fp 2226 1486 a(\)) p Fn(A) p Fp(\() p Fn(!) p Fp 2440 1486 a(;) p Fn 2480 1486 a(x;) p 2572 1486 a(y) p Fp 2620 1486 a(\)) p Fn(:) 448 1702 y @beginspecial @setspecial @endspecial Fo(Then,) p 713 1702 a(the) p 864 1702 a(op) p 951 1702 a(er) p 1026 1702 a(ator) p Fn 1222 1702 a(A) p Fh 1315 1702 a(7!) p Fn 1432 1702 a(@) p Fl 1480 1716 a(1) p Fn 1519 1702 a(A) p Fo 1620 1702 a(is) p 1718 1702 a(self-adjoint) p 2189 1702 a(with) p 2387 1702 a(domain) p Fh 1318 1918 a(D) p Fp 1391 1918 a(\() p Fn(@) p Fl 1474 1932 a(1) p Fp 1513 1918 a(\)) p 1574 1918 a(:=) p Fh 1695 1918 a(f) p Fn(A) p Fh 1834 1918 a(2) p 1920 1918 a(L) p Fl 1983 1880 a(2) p Fp 2062 1918 a(:) p Fn 2128 1918 a(@) p Fl 2176 1932 a(1) p Fn 2216 1918 a(A) p Fh 2309 1918 a(2) p 2395 1918 a(L) p Fl 2458 1880 a(2) p Fh 2497 1918 a(g) p Fn(:) 448 2333 y @beginspecial @setspecial @endspecial Fp(Therefore,) p 878 2333 a(Assumption) p 1371 2333 a(\(1.6\)) p 1578 2333 a(is) p 1660 2333 a(equiv) p 1868 2333 a(alen) m(t) p 2081 2333 a(to) p 2182 2333 a(the) p 2329 2333 a(statemen) m(t) p 2741 2333 a(that) p Fn 2928 2333 a(P) p Fj 2986 2347 a(\017) p Ff 3015 2358 a(F) p Fh 3095 2333 a(2) p 3181 2333 a(D) p Fp 3254 2333 a(\() p Fn(@) p Fl 3337 2347 a(1) p Fp 3377 2333 a(\).) 448 2582 y @beginspecial @setspecial @endspecial Fo(Pr) p 543 2582 a(o) p 584 2582 a(of.) p Fp 725 2582 a(Let) p Fn 878 2582 a(a) p Fp 952 2582 a(:=) p Fn 1073 2582 a(\031) p Fp 1128 2582 a(\() p Fn(A) p Fp(\).) p 1329 2582 a(Then,) p 1584 2582 a(\() p Fn(\031) p Fp 1674 2582 a(\() p Fn(@) p Fl 1757 2596 a(1) p Fn 1798 2582 a(A) p Fp(\)\)\() p Fn(!) s(;) p 2071 2582 a(x) p Fp(\)) p 2185 2582 a(=) p Fn 2281 2582 a(x) p Fl 2333 2596 a(1) p Fn 2372 2582 a(a) p Fp(\() p Fn(!) s(;) p 2555 2582 a(x) p Fp(\).) p 2706 2582 a(Th) m(us,) p 2954 2582 a(the) p 3101 2582 a(op) s(erator) p Fn 448 2707 a(A) p Fh 547 2707 a(7!) p Fn 668 2707 a(@) p Fl 716 2721 a(1) p Fn 756 2707 a(A) p Fp 858 2707 a(corresp) s(onds) p 1360 2707 a(to) p 1474 2707 a(the) p 1634 2707 a(m) m(ultiplication) p 2220 2707 a(op) s(erator) p 2590 2707 a(of) p Fn 2697 2707 a(x) p Fl 2749 2721 a(1) p Fp 2822 2707 a(on) 2972 2684 y(~) p Fh 2951 2707 a(L) p Fl 3014 2674 a(2) p Fp 3053 2707 a(,) p 3113 2707 a(whic) m(h) p 3376 2707 a(is) 448 2831 y(self-adjoin) m(t) p 916 2831 a(with) p 1123 2831 a(domain) p Fh 1446 2831 a(f) p Fn(a) p Fh 1565 2831 a(2) p Fp 1672 2808 a(~) p Fh 1651 2831 a(L) p Fl 1714 2798 a(2) p Fp 1793 2831 a(:) p Fn 1859 2831 a(x) p Fl 1911 2845 a(1) p Fn 1951 2831 a(a) p Fh 2024 2831 a(2) p Fp 2131 2808 a(~) p Fh 2110 2831 a(L) p Fl 2173 2798 a(2) p Fh 2212 2831 a(g) p Fp(.) p 2323 2767 V 2323 2856 4 89 v 2379 2856 V 2323 2859 60 4 v 589 3080 a @beginspecial @setspecial @endspecial(Next,) p 839 3080 a(w) m(e) p 974 3080 a(consider) p 1330 3080 a(an) p 1458 3080 a(op) s(erator) p 1826 3080 a(on) p Fh 1954 3080 a(L) p Fl 2017 3047 a(2) p Fp 2088 3080 a(whic) m(h) p 2350 3080 a(corresp) s(onds) p 2851 3080 a(to) p 2963 3080 a(taking) p 3245 3080 a(com-) 448 3205 y(m) m(utator) p 800 3205 a(with) p Fn 1007 3205 a(H) p Fj 1083 3219 a(!) r(;) p Fm(E) p Fp 1195 3205 a(.) p 1261 3205 a(The) p 1448 3205 a(matrix) p 1743 3205 a(elemen) m(t) p 2079 3205 a(of) p Fn 2183 3205 a(H) p Fj 2259 3219 a(!) r(;) p Fm(E) p Fp 2402 3205 a(is) p 2493 3205 a(giv) m(en) p 2731 3205 a(b) m(y) p Fn 929 3512 a(H) p Fj 1005 3526 a(!) r(;) p Fm(E) p Fp 1118 3512 a(\() p Fn(!) p Fp 1228 3512 a(;) p Fn 1268 3512 a(x;) p 1360 3512 a(y) p Fp 1408 3512 a(\)) p 1470 3512 a(=) p Fi 1566 3340 a(8) 1566 3415 y(<) 1566 3564 y(:) p Fp 1654 3399 a(1) p Fn(;) p Fp 2308 3399 a(\(if) p Fh 2427 3399 a(j) p Fn(x) p Fh 2524 3399 a(\000) p Fn 2615 3399 a(y) p Fh 2663 3399 a(j) p Fp 2714 3399 a(=) p 2810 3399 a(1\),) p Fn 1654 3512 a(\025V) p Fj 1760 3526 a(!) p Fp 1811 3512 a(\() p Fn(x) p Fp(\)) p 1954 3512 a(+) p Fh 2045 3512 a(E) p Fn 2101 3512 a(x) p Fl 2153 3526 a(1) p Fn 2192 3512 a(;) p Fp 2308 3512 a(\(if) p Fn 2427 3512 a(x) p Fp 2504 3512 a(=) p Fn 2600 3512 a(y) p Fp 2648 3512 a(\),) 1654 3625 y(0) p Fn(;) p Fp 2308 3625 a(\(otherwise\).) 448 3823 y @beginspecial @setspecial @endspecial(F) p 499 3823 a(or) p Fn 611 3823 a(A) p Fh 705 3823 a(2) p 791 3823 a(L) p Fl 854 3790 a(2) p Fp 893 3823 a(,) p 948 3823 a(w) m(e) p 1082 3823 a(de\014ne) p 1345 3823 a(\() p Fn(H) p Fj 1456 3837 a(!) r(;) p Fm(E) p Fn 1569 3823 a(A) p Fp(\)\() p Fn(!) p Fp 1783 3823 a(;) p Fn 1823 3823 a(x;) p 1915 3823 a(y) p Fp 1963 3823 a(\)) p 2029 3823 a(and) p 2206 3823 a(\() p Fn(AH) p Fj 2385 3837 a(!) r(;) p Fm(E) p Fp 2498 3823 a(\)\() p Fn(!) p Fp 2644 3823 a(;) p Fn 2684 3823 a(x;) p 2776 3823 a(y) p Fp 2824 3823 a(\)) p 2890 3823 a(as) p 3001 3823 a(\(2.3\)) 634 4039 y(\() p Fn(H) p Fj 745 4053 a(!) r(;) p Fm(E) p Fn 858 4039 a(A) p Fp(\)\() p Fn(!) p Fp 1071 4039 a(;) p Fn 1111 4039 a(x;) p 1203 4039 a(y) p Fp 1251 4039 a(\)) p 1313 4039 a(:=) p Fi 1504 3958 a(X) p Fm 1434 4147 a(j) p Fj(z) p Fm 1490 4147 a(\000) p Fj(x) p Fm(j) p Fl(=1) p Fn 1709 4039 a(A) p Fp(\() p Fn(!) p Fp 1887 4039 a(;) p Fn 1927 4039 a(z) t(;) p 2013 4039 a(y) p Fp 2061 4039 a(\)) p 2118 4039 a(+) p 2208 4039 a(\() p Fn(\025V) p Fj 2349 4053 a(!) p Fp 2400 4039 a(\() p Fn(x) p Fp(\)) p 2543 4039 a(+) p Fh 2634 4039 a(E) p Fn 2690 4039 a(x) p Fl 2742 4053 a(1) p Fp 2782 4039 a(\)) p Fn(A) p Fp(\() p Fn(!) p Fp 2995 4039 a(;) p Fn 3035 4039 a(x;) p 3127 4039 a(y) p Fp 3175 4039 a(\)) p Fn(;) p Fp 659 4294 a(\() p Fn(AH) p Fj 838 4308 a(!) r(;) p Fm(E) p Fp 951 4294 a(\)\() p Fn(!) p Fp 1096 4294 a(;) p Fn 1136 4294 a(x;) p 1228 4294 a(y) p Fp 1276 4294 a(\)) p 1338 4294 a(:=) p Fi 1527 4213 a(X) p Fm 1459 4401 a(j) p Fj(z) p Fm 1515 4401 a(\000) p Fj(y) p Fm 1607 4401 a(j) p Fl(=1) p Fn 1731 4294 a(A) p Fp(\() p Fn(!) p Fp 1910 4294 a(;) p Fn 1950 4294 a(x;) p 2042 4294 a(z) p Fp 2088 4294 a(\)) p 2144 4294 a(+) p 2235 4294 a(\() p Fn(\025V) p Fj 2376 4308 a(!) p Fp 2427 4294 a(\() p Fn(y) p Fp 2510 4294 a(\)) p 2566 4294 a(+) p Fh 2657 4294 a(E) p Fn 2713 4294 a(y) p Fl 2758 4308 a(1) p Fp 2797 4294 a(\)) p Fn(A) p Fp(\() p Fn(!) p Fp 3011 4294 a(;) p Fn 3051 4294 a(x;) p 3143 4294 a(y) p Fp 3191 4294 a(\)) p Fn(:) 448 4589 y @beginspecial @setspecial @endspecial Fp(W) p 533 4589 a(e) p 605 4589 a(de\014ne) 802 4805 y(\() p Fh(L) p Fj 900 4819 a(H) p Ff 958 4830 a(!) r(;) p Fd(E) p Fn 1063 4805 a(A) p Fp(\)\() p Fn(!) p Fp 1277 4805 a(;) p Fn 1317 4805 a(x;) p 1409 4805 a(y) p Fp 1457 4805 a(\)) p 1518 4805 a(:=) p 1640 4805 a(\() p Fn(H) p Fj 1751 4819 a(!) r(;) p Fm(E) p Fn 1864 4805 a(A) p Fp(\)\() p Fn(!) p Fp 2077 4805 a(;) p Fn 2117 4805 a(x;) p 2209 4805 a(y) p Fp 2257 4805 a(\)) p Fh 2314 4805 a(\000) p Fp 2404 4805 a(\() p Fn(AH) p Fj 2583 4819 a(!) r(;) p Fm(E) p Fp 2697 4805 a(\)\() p Fn(!) p Fp 2842 4805 a(;) p Fn 2882 4805 a(x;) p 2974 4805 a(y) p Fp 3022 4805 a(\)) p Fn(;) p Fp 448 4805 a(\(2.13\)) 1897 5225 y(16) p eop %%Page: 17 17 17 16 bop 448 573 a @beginspecial @setspecial @endspecial Fp(whic) m(h) p 704 573 a(mak) m(es) p 972 573 a(sense) p 1201 573 a(as) p 1308 573 a(a) p 1379 573 a(function) p 1730 573 a(on) p 1852 573 a(\012) p Fh 1929 573 a(\002) p Fk 2011 573 a(Z) p 2031 573 a(Z) p Fj 2085 536 a(d) p Fh 2136 573 a(\002) p Fk 2218 573 a(Z) p 2238 573 a(Z) p Fj 2292 536 a(d) p Fp 2333 573 a(.) p 2397 573 a(W) p 2482 573 a(e) p 2549 573 a(note) p 2746 573 a(\() p Fh(L) p Fj 2844 587 a(H) p Ff 2902 598 a(!) r(;) p Fd(E) p Fn 3007 573 a(A) p Fp(\)\() p Fn(!) p Fp 3221 573 a(;) p Fn 3261 573 a(x;) p 3353 573 a(y) p Fp 3401 573 a(\)) 448 697 y(satis\014es) p 789 697 a(\(CR\),) p 1054 697 a(though) p 1369 697 a(\() p Fn(H) p Fj 1480 711 a(!) r(;) p Fm(E) p Fn 1593 697 a(A) p Fp(\)\() p Fn(!) p Fp 1807 697 a(;) p Fn 1847 697 a(x;) p 1939 697 a(y) p Fp 1987 697 a(\)) p 2059 697 a(and) p 2242 697 a(\() p Fn(AH) p Fj 2421 711 a(!) r(;) p Fm(E) p Fp 2534 697 a(\)\() p Fn(!) p Fp 2680 697 a(;) p Fn 2720 697 a(x;) p 2812 697 a(y) p Fp 2860 697 a(\)) p 2932 697 a(do) p 3065 697 a(not.) p 3281 697 a(The) 448 822 y(corresp) s(onding) p 1033 822 a(elemen) m(t) p 1369 822 a(in) 1496 799 y(~) p Fh 1475 822 a(L) p Fl 1538 789 a(2) p Fp 1607 822 a(is) p Fn 767 1038 a(\031) p Fi 822 944 a(\020) p Fh 871 1038 a(L) p Fj 934 1052 a(H) p Ff 992 1063 a(!) r(;) p Fd(E) p Fn 1097 1038 a(A) p Fi 1165 944 a(\021) p Fp 1215 1038 a(\() p Fn(!) s(;) p 1350 1038 a(x) p Fp(\)) p 1463 1038 a(=) p Fi 1629 957 a(X) p Fm 1559 1145 a(j) p Fj(z) p Fm 1615 1145 a(\000) p Fj(x) p Fm(j) p Fl(=1) p Fn 1834 1038 a(a) p Fp(\() p Fn(!) s(;) p 2017 1038 a(z) p Fp 2063 1038 a(\)) p 2119 1038 a(+) p 2210 1038 a(\() p Fn(\025V) p Fj 2351 1052 a(!) p Fp 2402 1038 a(\() p Fn(x) p Fp(\)) p 2545 1038 a(+) p Fh 2636 1038 a(E) p Fn 2692 1038 a(x) p Fl 2744 1052 a(1) p Fp 2783 1038 a(\)) p Fn(a) p Fp(\() p Fn(!) s(;) p 3001 1038 a(x) p Fp(\)) p 448 1038 a(\(2.14\)) p Fh 1463 1301 a(\000) p Fi 1559 1207 a(n) 1637 1220 y(X) p Fm 1615 1408 a(j) p Fj(z) p Fm 1671 1408 a(j) p Fl(=1) p Fn 1795 1301 a(a) p Fp(\() p Fn(T) p Fm 1944 1263 a(\000) p Fj(z) p Fn 2039 1301 a(!) s(;) p 2139 1301 a(x) p Fh 2211 1301 a(\000) p Fn 2302 1301 a(z) p Fp 2348 1301 a(\)) p 2404 1301 a(+) p Fn 2495 1301 a(\025V) p Fj 2601 1315 a(!) p Fp 2651 1301 a(\(0\)) p Fn(a) p Fp(\() p Fn(!) s(;) p 2949 1301 a(x) p Fp(\)) p Fi 3036 1207 a(o) p Fn 3094 1301 a(:) 448 1608 y @beginspecial @setspecial @endspecial Fp(Since) p Fe 696 1608 a(E) p Fh(j) p Fn(V) p Fj 843 1622 a(!) p Fp 894 1608 a(\(0\)) p Fh(j) p Fl 1034 1575 a(2) p Fn 1118 1608 a(<) p Fh 1232 1608 a(1) p Fp(,) p Fh 1392 1608 a(L) p Fj 1455 1622 a(H) p Ff 1513 1633 a(!) r(;) p Fd(E) p Fn 1618 1608 a(A) p Fh 1729 1608 a(2) p 1833 1608 a(L) p Fl 1896 1575 a(2) p Fp 1976 1608 a(if) p Fn 2071 1608 a(A) p Fh 2182 1608 a(2) p 2286 1608 a(A) p Fl 2359 1622 a(0) p Fp 2398 1608 a(.) p 2496 1608 a(Hence) p Fh 2777 1608 a(L) p Fj 2840 1622 a(H) p Ff 2898 1633 a(!) r(;) p Fd(E) p Fp 3044 1608 a(is) p 3146 1608 a(densely) 448 1733 y(de\014ned) p 761 1733 a(on) p Fh 888 1733 a(L) p Fl 951 1700 a(2) p Fp 990 1733 a(.) p Fe 448 1932 a(Prop) s(osition) p 1014 1932 a(2.7) p 1193 1932 a @beginspecial @setspecial @endspecial Fo(\(1\)) p Fh 1346 1932 a(L) p Fj 1409 1946 a(H) p Ff 1467 1957 a(!) r(;) p Fd(E) p Fo 1604 1932 a(is) p 1702 1932 a(self-adjoint) p 2174 1932 a(with) p 2371 1932 a(domain) p Fh 687 2164 a(D) p Fp 760 2164 a(\() p Fh(L) p Fj 858 2178 a(H) p Ff 916 2189 a(!) r(;) p Fd(E) p Fp 1021 2164 a(\)) p 1082 2164 a(:=) p Fi 1203 2070 a(n) p Fn 1259 2164 a(A) p Fh 1352 2164 a(2) p 1438 2164 a(L) p Fl 1501 2127 a(2) p Fp 1565 2164 a(:) p Fi 1203 2253 a(\020) p Fn 1253 2347 a(\025) p Fp(\() p Fn(V) p Fj 1394 2361 a(!) p Fp 1445 2347 a(\() p Fn(x) p Fp(\)) p Fh 1587 2347 a(\000) p Fn 1678 2347 a(V) p Fj 1731 2361 a(!) p Fp 1782 2347 a(\() p Fn(y) p Fp 1865 2347 a(\)\)) p 1956 2347 a(+) p Fh 2047 2347 a(E) p Fp 2103 2347 a(\() p Fn(x) p Fl 2190 2361 a(1) p Fh 2250 2347 a(\000) p Fn 2341 2347 a(y) p Fl 2386 2361 a(1) p Fp 2425 2347 a(\)) p Fi 2460 2253 a(\021) p Fn 2510 2347 a(A) p Fp(\() p Fn(!) p Fp 2688 2347 a(;) p Fn 2728 2347 a(x;) p 2820 2347 a(y) p Fp 2868 2347 a(\)) p Fh 2929 2347 a(2) p 3015 2347 a(L) p Fl 3078 2309 a(2) p Fi 3117 2253 a(o) p Fn 3173 2347 a(:) 589 2591 y @beginspecial @setspecial @endspecial Fo(\(2\)) p Fn 743 2591 a(e) p Fj 785 2544 a(it) p Fm(L) p Ff 883 2555 a(H) 933 2572 y(!) r(;) p Fd(E) p Fn 1042 2591 a(A) p Fp 1136 2591 a(=) p Fn 1232 2591 a(e) p Fj 1274 2558 a(itH) p Ff 1381 2569 a(!) r(;) p Fd(E) p Fn 1487 2591 a(Ae) p Fm 1597 2558 a(\000) p Fj(itH) p Ff 1759 2569 a(!) r(;) p Fd(E) p Fo 1865 2591 a(,) p Fn 1926 2591 a(A) p Fh 2019 2591 a(2) p 2105 2591 a(L) p Fl 2168 2558 a(2) p Fo 2207 2591 a(.) p Fe 448 2815 a(Remark) p 846 2815 a(2.4) p 1025 2815 a @beginspecial @setspecial @endspecial Fn(H) p Fj 1101 2829 a(!) r(;) p Fm(E) p Fo 1246 2815 a(has) p 1408 2815 a(the) p 1559 2815 a(fol) p 1661 2815 a(lowing) p 1945 2815 a(pr) p 2024 2815 a(op) p 2111 2815 a(erty) p Fn 944 3031 a(U) p Fp 1016 3031 a(\() p Fn(a) p Fp(\)) p Fn(H) p Fj 1210 3045 a(!) r(;) p Fm(E) p Fn 1323 3031 a(U) p Fp 1395 3031 a(\() p Fn(a) p Fp(\)) p Fm 1513 2994 a(\003) p Fp 1579 3031 a(=) p Fn 1675 3031 a(H) p Fj 1751 3045 a(T) p Ff 1802 3026 a(a) p Fj 1839 3045 a(!) r(;) p Fm(E) p Fh 1972 3031 a(\000) p 2063 3031 a(E) p Fn 2119 3031 a(a) p Fl 2167 3045 a(1) p Fn 2207 3031 a(;) p 2340 3031 a(!) p Fh 2425 3031 a(2) p Fp 2511 3031 a(\012) p Fn(;) p 2642 3031 a(a) p Fh 2716 3031 a(2) p Fk 2802 3031 a(Z) p 2821 3031 a(Z) p Fj 2876 2994 a(d) p Fn 2916 3031 a(;) p Fp 448 3031 a(\(2.15\)) 448 3247 y @beginspecial @setspecial @endspecial Fo(which) p 704 3247 a(implies) p Fn 1230 3372 a(U) p Fp 1302 3372 a(\() p Fn(a) p Fp(\)) p Fn(e) p Fj 1462 3334 a(itH) p Ff 1569 3345 a(!) r(;) p Fd(E) p Fn 1676 3372 a(U) p Fp 1748 3372 a(\() p Fn(a) p Fp(\)) p Fm 1866 3334 a(\003) p Fp 1931 3372 a(=) p Fn 2027 3372 a(e) p Fj 2069 3334 a(itH) p Ff 2176 3347 a(T) 2220 3333 y(a) 2259 3347 y(!) r(;) p Fd(E) p Fn 2364 3372 a(e) p Fm 2406 3334 a(\000) p Fj(it) p Fm(E) p Fj 2553 3334 a(a) p Fc 2590 3343 a(1) p Fn 2630 3372 a(:) p Fp 448 3372 a(\(2.16\)) 448 3550 y @beginspecial @setspecial @endspecial Fo(However,) p 852 3550 a(by) p 974 3550 a(using) p 1217 3550 a(\(2.16\),) p 1524 3550 a(we) p 1663 3550 a(c) p 1700 3550 a(an) p 1834 3550 a(show) p Fp 2061 3550 a(\() p Fn(e) p Fj 2138 3517 a(itH) p Ff 2245 3528 a(!) r(;) p Fd(E) p Fn 2352 3550 a(Ae) p Fm 2462 3517 a(\000) p Fj(itH) p Ff 2624 3528 a(!) r(;) p Fd(E) p Fp 2730 3550 a(\)\() p Fn(!) p Fp 2876 3550 a(;) p Fn 2916 3550 a(x;) p 3008 3550 a(y) p Fp 3056 3550 a(\)) p Fo 3128 3550 a(satis\014es) 448 3675 y(\(CR\)) p 685 3675 a(\() p 753 3675 a(it) p 842 3675 a(is) p 938 3675 a(str) p 1038 3675 a(aightforwar) p 1481 3675 a(d) p 1562 3675 a(if) p Fn 1649 3675 a(A) p Fh 1742 3675 a(2) p 1828 3675 a(A) p Fo(.) p 1970 3675 a(F) p 2022 3675 a(or) p Fn 2138 3675 a(A) p Fh 2231 3675 a(2) p 2317 3675 a(L) p Fl 2380 3642 a(2) p Fo 2419 3675 a(,) p 2478 3675 a(we) p 2611 3675 a(use) p 2770 3675 a(Pr) p 2865 3675 a(op) p 2952 3675 a(osition) p 3251 3675 a(2.3\).) 448 3799 y(By) p 581 3799 a(using) p 812 3799 a(the) p 955 3799 a(ar) p 1034 3799 a(gument) p 1347 3799 a(in) p 1451 3799 a(the) p 1593 3799 a(pr) p 1672 3799 a(o) p 1713 3799 a(of) p 1814 3799 a(of) p 1913 3799 a(Pr) p 2008 3799 a(op) p 2095 3799 a(osition) p 2388 3799 a(2.5,) p Fn 2563 3799 a(e) p Fj 2605 3766 a(itH) p Ff 2712 3777 a(!) r(;) p Fd(E) p Fn 2818 3799 a(Ae) p Fm 2928 3766 a(\000) p Fj(itH) p Ff 3090 3777 a(!) r(;) p Fd(E) p Fh 3221 3799 a(2) p 3307 3799 a(L) p Fl 3370 3766 a(2) p Fo 3409 3799 a(,) 448 3924 y(for) p Fn 594 3924 a(A) p Fh 687 3924 a(2) p 773 3924 a(L) p Fl 836 3891 a(2) p Fo 875 3924 a(.) 448 4148 y @beginspecial @setspecial @endspecial(Pr) p 543 4148 a(o) p 584 4148 a(of) p 710 4148 a(of) p 835 4148 a(Pr) p 930 4148 a(op) p 1017 4148 a(osition) p 1335 4148 a(2.7\(1\)) p Fp 1677 4148 a(It) p 1794 4148 a(is) p 1905 4148 a(easy) p 2124 4148 a(to) p 2254 4148 a(see) p 2421 4148 a(the) p 2596 4148 a(op) s(erators) p Fn 3018 4148 a(a) p Fp(\() p Fn(!) s(;) p 3201 4148 a(x) p Fp(\)) p Fh 3346 4148 a(7!) p Fi 448 4208 a(P) p Fm 536 4295 a(j) p Fj(z) p Fm 592 4295 a(\000) p Fj(x) p Fm(j) p Fl(=1) p Fn 815 4272 a(a) p Fp(\() p Fn(!) s(;) p 998 4272 a(z) p Fp 1044 4272 a(\),) p 1172 4272 a(and) p Fn 1378 4272 a(a) p Fp(\() p Fn(!) s(;) p 1561 4272 a(x) p Fp(\)) p Fh 1722 4272 a(7!) p Fi 1887 4208 a(P) p Fm 1974 4295 a(j) p Fj(z) p Fm 2030 4295 a(j) p Fl(=1) p Fn 2158 4272 a(a) p Fp(\() p Fn(T) p Fm 2307 4240 a(\000) p Fj(z) p Fn 2402 4272 a(!) s(;) p 2502 4272 a(x) p Fh 2594 4272 a(\000) p Fn 2704 4272 a(z) p Fp 2750 4272 a(\),) p 2878 4272 a(whic) m(h) p 3167 4272 a(app) s(ear) 448 4397 y(in) p 574 4397 a(\(2.14\),) p 886 4397 a(are) p 1058 4397 a(b) s(ounded) p 1449 4397 a(on) 1616 4374 y(~) p Fh 1595 4397 a(L) p Fl 1658 4364 a(2) p Fp 1697 4397 a(.) p 1821 4397 a(The) p 2028 4397 a(m) m(ultiplication) p 2631 4397 a(op) s(erator) p Fn 3017 4397 a(a) p Fp(\() p Fn(!) s(;) p 3200 4397 a(x) p Fp(\)) p Fh 3346 4397 a(7!) p Fi 448 4427 a(\020) p Fn 498 4522 a(\025) p Fp(\() p Fn(V) p Fj 639 4536 a(!) p Fp 690 4522 a(\() p Fn(x) p Fp(\)) p Fh 833 4522 a(\000) p Fn 924 4522 a(V) p Fj 977 4536 a(!) p Fp 1027 4522 a(\(0\)\)) p 1199 4522 a(+) p Fh 1290 4522 a(E) p Fn 1346 4522 a(x) p Fl 1398 4536 a(1) p Fi 1437 4427 a(\021) p Fn 1487 4522 a(a) p Fp(\() p Fn(!) s(;) p 1670 4522 a(x) p Fp(\)) p 1788 4522 a(is) p 1879 4522 a(clearly) p 2170 4522 a(self-adjoin) m(t) p 2638 4522 a(with) p 2845 4522 a(domain) p Fh 835 4771 a(D) p Fp 933 4771 a(:=) p Fi 1054 4676 a(n) p Fn 1110 4771 a(a) p Fh 1183 4771 a(2) p Fp 1290 4748 a(~) p Fh 1269 4771 a(L) p Fl 1332 4733 a(2) p Fp 1396 4771 a(:) p Fi 1447 4676 a(\020) p Fn 1496 4771 a(\025) p Fp(\() p Fn(V) p Fj 1637 4785 a(!) p Fp 1688 4771 a(\() p Fn(x) p Fp(\)) p Fh 1831 4771 a(\000) p Fn 1922 4771 a(V) p Fj 1975 4785 a(!) p Fp 2026 4771 a(\(0\)\)) p 2197 4771 a(+) p Fh 2288 4771 a(E) p Fn 2344 4771 a(x) p Fl 2396 4785 a(1) p Fi 2436 4676 a(\021) p Fn 2485 4771 a(a) p Fp(\() p Fn(!) s(;) p 2668 4771 a(x) p Fp(\)) p Fh 2781 4771 a(2) p Fp 2889 4748 a(~) p Fh 2867 4771 a(L) p Fl 2930 4733 a(2) p Fi 2969 4676 a(o) p Fn 3025 4771 a(:) p Fp 1897 5225 a(17) p eop %%Page: 18 18 18 17 bop 448 573 a @beginspecial @setspecial @endspecial Fp(Therefore,) p Fh 886 573 a(L) p Fj 949 587 a(H) p Ff 1007 598 a(!) r(;) p Fd(E) p Fp 1142 573 a(is) p 1233 573 a(self-adjoin) m(t) p 1701 573 a(with) p 1908 573 a(domain) p Fn 2231 573 a(\031) p Fm 2286 540 a(\000) p Fl(1) p Fh 2381 573 a(D) p Fp 2479 573 a(=) p Fh 2575 573 a(D) p Fp 2648 573 a(\() p Fh(L) p Fj 2746 587 a(H) p Ff 2804 598 a(!) r(;) p Fd(E) p Fp 2909 573 a(\).) p 3010 509 60 4 v 3010 598 4 89 v 3065 598 V 3010 601 60 4 v 589 788 a @beginspecial @setspecial @endspecial(T) p 647 788 a(o) p 741 788 a(pro) m(v) m(e) p 1003 788 a(Prop) s(osition) p 1510 788 a(2.7\(2\),) p 1820 788 a(w) m(e) p 1971 788 a(prepare) p 2317 788 a(the) p 2491 788 a(follo) m(wing) p 2892 788 a(Lemma.) p 3305 788 a(Let) p Fh 448 913 a(D) p Fp 521 913 a(\() p Fn(H) p Fj 632 927 a(!) r(;) p Fm(E) p Fp 745 913 a(\)) p 819 913 a(b) s(e) p 951 913 a(the) p 1116 913 a(domain) p 1447 913 a(of) p 1559 913 a(the) p 1724 913 a(self-adjoin) m(t) p 2200 913 a(op) s(erator) p Fn 2575 913 a(H) p Fj 2651 927 a(!) r(;) p Fm(E) p Fp 2803 913 a(on) p Fn 2937 913 a(l) p Fl 2966 880 a(2) p Fp 3005 913 a(\() p Fk(Z) p 3060 913 a(Z) p Fj 3116 876 a(d) p Fp 3156 913 a(\)) p 3230 913 a(giv) m(en) 448 1037 y(b) m(y) p Fh 878 1162 a(D) p Fp 951 1162 a(\() p Fn(H) p Fj 1062 1176 a(!) r(;) p Fm(E) p Fp 1175 1162 a(\)) p 1236 1162 a(:=) p Fh 1357 1162 a(f) p Fn(') p Fh 1487 1162 a(2) p Fn 1573 1162 a(l) p Fl 1602 1124 a(2) p Fp 1641 1162 a(\() p Fk(Z) p 1696 1162 a(Z) p Fj 1751 1124 a(d) p Fp 1792 1162 a(\)) p 1852 1162 a(:) p 1903 1162 a(\() p Fn(\025V) p Fj 2044 1176 a(!) p Fp 2095 1162 a(\() p Fn(x) p Fp(\)) p 2238 1162 a(+) p Fh 2329 1162 a(E) p Fn 2385 1162 a(x) p Fl 2437 1176 a(1) p Fp 2476 1162 a(\)) p Fn(') p Fh 2596 1162 a(2) p Fn 2682 1162 a(l) p Fl 2711 1124 a(2) p Fp 2750 1162 a(\() p Fk(Z) p 2805 1162 a(Z) p Fj 2860 1124 a(d) p Fp 2901 1162 a(\)) p Fh(g) p Fn(:) p Fe 448 1361 a(Lemma) p 819 1361 a(2.4) p 998 1361 a @beginspecial @setspecial @endspecial Fo(Supp) p 1185 1361 a(ose) p Fn 1353 1361 a(') p Fh 1453 1361 a(2) p 1554 1361 a(D) p Fp 1627 1361 a(\() p Fn(H) p Fj 1738 1375 a(!) r(;) p Fm(E) p Fp 1851 1361 a(\)) p Fo 1927 1361 a(for) p 2081 1361 a(any) p Fn 2264 1361 a(!) p Fh 2364 1361 a(2) p Fp 2466 1361 a(\012) p Fo(,) p 2602 1361 a(and) p Fn 2787 1361 a(A) p Fh 2896 1361 a(2) p 2997 1361 a(A) p Fl 3070 1375 a(0) p Fo 3110 1361 a(.) p 3205 1361 a(Then,) p Fn 448 1486 a(A') p Fh 601 1486 a(2) p 687 1486 a(D) p Fp 760 1486 a(\() p Fn(H) p Fj 871 1500 a(!) r(;) p Fm(E) p Fp 984 1486 a(\)) p Fo 1052 1486 a(for) p 1197 1486 a(any) p Fn 1371 1486 a(!) p Fh 1456 1486 a(2) p Fp 1542 1486 a(\012) p Fo(.) 448 1735 y @beginspecial @setspecial @endspecial(Pr) p 543 1735 a(o) p 584 1735 a(of.) p Fp 728 1735 a(W) p 813 1735 a(e) p 885 1735 a(ha) m(v) m(e) p 1094 1735 a(only) p 1294 1735 a(to) p 1405 1735 a(sho) m(w) 722 1951 y(\() p Fn(\025V) p Fj 863 1965 a(!) p Fp 914 1951 a(\() p Fn(x) p Fp(\)) p 1057 1951 a(+) p Fh 1148 1951 a(E) p Fn 1204 1951 a(x) p Fl 1256 1965 a(1) p Fp 1295 1951 a(\)\() p Fn(A') p Fp(\)\() p Fn(x) p Fp(\)) p 1677 1951 a(=) p 1773 1951 a(\() p Fn(\025V) p Fj 1914 1965 a(!) p Fp 1965 1951 a(\() p Fn(x) p Fp(\)) p 2107 1951 a(+) p Fh 2198 1951 a(E) p Fn 2254 1951 a(x) p Fl 2306 1965 a(1) p Fp 2346 1951 a(\)) p Fi 2426 1870 a(X) p Fj 2396 2068 a(y) p Fm 2433 2068 a(2) p Fg(Z) p 2496 2068 a(Z) p Ff 2540 2043 a(d) p Fn 2591 1951 a(A) p Fp(\() p Fn(!) p Fp 2769 1951 a(;) p Fn 2809 1951 a(x;) p 2901 1951 a(y) p Fp 2949 1951 a(\)) p Fn(') p Fp(\() p Fn(y) p Fp 3126 1951 a(\)) p Fh 1682 2206 a(2) p Fn 1773 2206 a(l) p Fl 1802 2169 a(2) p Fp 1841 2206 a(\() p Fk(Z) p 1896 2206 a(Z) p Fj 1951 2169 a(d) p Fp 1992 2206 a(\)) p Fn(;) 448 2422 y @beginspecial @setspecial @endspecial Fp(for) p 584 2422 a(an) m(y) p Fn 753 2422 a(!) p Fh 838 2422 a(2) p Fp 924 2422 a(\012.) p 1054 2422 a(Since) p Fn 1288 2422 a(A) p Fh 1382 2422 a(2) p 1468 2422 a(A) p Fl 1541 2436 a(0) p Fp 1580 2422 a(,) p 1633 2422 a(there) p 1862 2422 a(exist) p 2074 2422 a(constan) m(ts) p Fn 2474 2422 a(C) p 2571 2422 a(>) p Fp 2667 2422 a(0,) p Fn 2765 2422 a(K) p 2874 2422 a(>) p Fp 2970 2422 a(0,) p 3068 2422 a(suc) m(h) p 3270 2422 a(that) p Fh 448 2547 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 652 2547 a(;) p Fn 692 2547 a(x;) p 784 2547 a(y) p Fp 832 2547 a(\)) p Fh(j) p 919 2547 a(\024) p Fn 1015 2547 a(C) p Fp 1087 2547 a(,) p 1142 2547 a(and) p Fn 1318 2547 a(A) p Fp(\() p Fn(!) p Fp 1497 2547 a(;) p Fn 1537 2547 a(x;) p 1629 2547 a(y) p Fp 1677 2547 a(\)) p 1738 2547 a(=) p 1834 2547 a(0) p 1910 2547 a(if) p Fh 1993 2547 a(j) p Fn(x) p Fh 2091 2547 a(\000) p Fn 2181 2547 a(y) p Fh 2229 2547 a(j) p Fn 2280 2547 a(>) p 2376 2547 a(K) p Fp 2460 2547 a(.) p 2525 2547 a(Then,) p Fh 836 2763 a(j) p Fp(\() p Fn(\025V) p Fj 1002 2777 a(!) p Fp 1053 2763 a(\() p Fn(x) p Fp(\)) p 1196 2763 a(+) p Fh 1287 2763 a(E) p Fn 1343 2763 a(x) p Fl 1395 2777 a(1) p Fp 1434 2763 a(\)) p Fi 1515 2682 a(X) p Fj 1485 2880 a(y) p Fm 1522 2880 a(2) p Fg(Z) p 1585 2880 a(Z) p Ff 1628 2855 a(d) p Fn 1679 2763 a(A) p Fp(\() p Fn(!) p Fp 1858 2763 a(;) p Fn 1898 2763 a(x;) p 1990 2763 a(y) p Fp 2038 2763 a(\)) p Fn(') p Fp(\() p Fn(y) p Fp 2215 2763 a(\)) p Fh(j) 1539 3024 y(\024) p Fn 1679 3024 a(C) p Fh 1751 3024 a(j) p Fp(\() p Fn(\025V) p Fj 1917 3038 a(!) p Fp 1968 3024 a(\() p Fn(x) p Fp(\)) p 2111 3024 a(+) p Fh 2202 3024 a(E) p Fn 2258 3024 a(x) p Fl 2310 3038 a(1) p Fp 2349 3024 a(\)) p Fh(j) p Fi 2462 2943 a(X) p Fm 2425 3131 a(j) p Fj(z) p Fm 2481 3131 a(j\024) p Fj(K) p Fh 2634 3024 a(j) p Fn(') p Fp(\() p Fn(x) p Fp 2826 3024 a(+) p Fn 2917 3024 a(z) p Fp 2963 3024 a(\)) p Fh(j) p Fn(:) 448 3339 y @beginspecial @setspecial @endspecial Fp(W) p 533 3339 a(e) p 611 3339 a(will) p 789 3339 a(sho) m(w) p Fh 1020 3339 a(j) p Fp(\() p Fn(\025V) p Fj 1186 3353 a(!) p Fp 1237 3339 a(\() p Fn(x) p Fp(\)) p 1384 3339 a(+) p Fh 1479 3339 a(E) p Fn 1535 3339 a(x) p Fl 1587 3353 a(1) p Fp 1626 3339 a(\)) p Fn(') p Fp(\() p Fn(x) p Fp 1833 3339 a(+) p Fn 1928 3339 a(z) p Fp 1974 3339 a(\)) p Fh(j) p 2070 3339 a(2) p Fn 2166 3339 a(l) p Fl 2195 3306 a(2) p Fp 2234 3339 a(\() p Fk(Z) p 2289 3339 a(Z) p Fj 2344 3302 a(d) p Fp 2385 3339 a(\),) p 2483 3339 a(w.r.t.) p Fn 2754 3339 a(x) p Fp 2842 3339 a(for) p 2987 3339 a(an) m(y) p 3165 3339 a(\014xed) p Fn 3391 3339 a(z) p Fp 448 3463 a(\() p Fh(j) p Fn(z) p Fh 554 3463 a(j) p 606 3463 a(\024) p Fn 702 3463 a(K) p Fp 786 3463 a(\)) p 851 3463 a(whic) m(h) p 1111 3463 a(completes) p 1531 3463 a(the) p 1687 3463 a(pro) s(of.) p 1960 3463 a(In) p 2074 3463 a(fact,) p 2279 3463 a(letting) p Fn 2566 3463 a(y) p Fp 2640 3463 a(=) p Fn 2735 3463 a(x) p Fp 2808 3463 a(+) p Fn 2899 3463 a(z) p Fp 2945 3463 a(,) p Fh 728 3679 a(j) p Fp(\() p Fn(\025V) p Fj 894 3693 a(!) p Fp 946 3679 a(\() p Fn(x) p Fp(\)) p 1088 3679 a(+) p Fh 1179 3679 a(E) p Fn 1235 3679 a(x) p Fl 1287 3693 a(1) p Fp 1370 3679 a(\)) p Fn 1448 3679 a(') p Fp(\() p Fn(x) p Fp 1615 3679 a(+) p Fn 1706 3679 a(z) p Fp 1752 3679 a(\)) p Fh(j) p Fp 1352 3829 a(=) p Fh 1448 3829 a(j) p Fn(\025V) p Fj 1579 3848 a(T) p Fd 1630 3829 a(\000) p Ff(x) p Fc(+) p Ff(y) p Fj 1797 3848 a(!) p Fp 1847 3829 a(\() p Fn(y) p Fp 1930 3829 a(\)) p 1986 3829 a(+) p Fh 2077 3829 a(E) p Fn 2133 3829 a(y) p Fl 2178 3843 a(1) p Fp 2237 3829 a(+) p Fh 2328 3829 a(E) p Fp 2384 3829 a(\() p Fn(x) p Fl 2471 3843 a(1) p Fh 2531 3829 a(\000) p Fn 2622 3829 a(y) p Fl 2667 3843 a(1) p Fp 2706 3829 a(\)) p Fh(jj) p Fn(') p Fp(\() p Fn(x) p Fp 2959 3829 a(+) p Fn 3050 3829 a(z) p Fp 3096 3829 a(\)) p Fh(j) 1352 3978 y(\024) p 1448 3978 a(j) p Fn(\025V) p Fj 1579 3992 a(T) p Ff 1630 3973 a(z) p Fj 1666 3992 a(!) p Fp 1716 3978 a(\() p Fn(y) p Fp 1799 3978 a(\)) p 1855 3978 a(+) p Fh 1946 3978 a(E) p Fn 2002 3978 a(y) p Fl 2047 3992 a(1) p Fh 2086 3978 a(jj) p Fn(') p Fp(\() p Fn(y) p Fp 2278 3978 a(\)) p Fh(j) p Fp 2360 3978 a(+) p Fh 2451 3978 a(jE) p Fn 2532 3978 a(z) p Fl 2574 3992 a(1) p Fh 2614 3978 a(jj) p Fn(') p Fp(\() p Fn(y) p Fp 2806 3978 a(\)) p Fh(j) p Fn(:) 448 4194 y @beginspecial @setspecial @endspecial Fp(By) p 595 4194 a(assumption,) p 1106 4194 a(the) p 1266 4194 a(\014rst) p 1458 4194 a(term) p 1679 4194 a(of) p 1787 4194 a(the) p 1947 4194 a(RHS) p 2167 4194 a(in) p 2277 4194 a(the) p 2438 4194 a(ab) s(o) m(v) m(e) p 2699 4194 a(expression) p 3141 4194 a(b) s(elongs) 448 4318 y(to) p Fn 559 4318 a(l) p Fl 588 4285 a(2) p Fp 628 4318 a(\() p Fk(Z) p 683 4318 a(Z) p Fj 738 4282 a(d) p Fp 778 4318 a(\),) p 869 4318 a(for) p 1008 4318 a(an) m(y) p Fn 1180 4318 a(!) p Fh 1265 4318 a(2) p Fp 1351 4318 a(\012.) p 1482 4254 V 1482 4343 4 89 v 1538 4343 V 1482 4346 60 4 v 448 4568 a @beginspecial @setspecial @endspecial Fo(Pr) p 543 4568 a(o) p 584 4568 a(of) p 698 4568 a(of) p 811 4568 a(Pr) p 906 4568 a(op) p 993 4568 a(osition) p 1301 4568 a(2.7) p 1460 4568 a(\(2\)) p Fp 1657 4568 a(Let) p Fn 1826 4568 a(U) p Fp 1898 4568 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fp 2106 4568 a(:=) p Fn 2238 4568 a(e) p Fj 2280 4535 a(itH) p Ff 2387 4546 a(!) r(;) p Fd(E) p Fn 2494 4568 a(Ae) p Fm 2604 4535 a(\000) p Fj(itH) p Ff 2766 4546 a(!) r(;) p Fd(E) p Fp 2872 4568 a(,) p Fn 2936 4568 a(A) p Fh 3040 4568 a(2) p 3137 4568 a(L) p Fl 3200 4535 a(2) p Fp 3239 4568 a(.) p 3325 4568 a(By) 448 4692 y(Prop) s(osition) p 947 4692 a(2.5) p 1103 4692 a(and) p 1290 4692 a(Remark) p 1642 4692 a(2.4,) p Fn 1826 4692 a(U) p Fp 1898 4692 a(\() p Fn(t) p Fp(\)) p 2041 4692 a(is) p 2142 4692 a(uniformly) p 2566 4692 a(b) s(ounded) p 2947 4692 a(on) p Fh 3083 4692 a(L) p Fl 3146 4659 a(2) p Fp 3225 4692 a(w.r.t.) p Fn 448 4817 a(t) p Fh 527 4817 a(2) p Fp 633 4817 a(I) p 651 4817 a(R) o(.) p 820 4817 a(Th) m(us,) p 1090 4817 a(it) p 1193 4817 a(su\016ces) p 1515 4817 a(to) p 1638 4817 a(sho) m(w) p Fn 1875 4817 a(e) p Fj 1917 4769 a(it) p Fm(L) p Ff 2015 4780 a(H) 2065 4797 y(!) r(;) p Fd(E) p Fn 2175 4817 a(A) p Fp 2289 4817 a(=) p Fn 2405 4817 a(U) p Fp 2477 4817 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fp(,) p 2719 4817 a(for) p Fn 2871 4817 a(A) p Fh 2984 4817 a(2) p 3090 4817 a(A) p Fl 3163 4831 a(0) p Fp 3202 4817 a(.) p 3305 4817 a(Let) 1897 5225 y(18) p eop %%Page: 19 19 19 18 bop Fn 448 573 a(') p Fh 533 573 a(2) p 619 573 a(D) p Fp 692 573 a(\() p Fn(H) p Fj 803 587 a(!) r(;) p Fm(E) p Fp 915 573 a(\)) p 981 573 a(for) p 1120 573 a(an) m(y) p Fn 1292 573 a(!) p Fh 1377 573 a(2) p Fp 1463 573 a(\012,) p 1584 573 a(and) p Fn 1761 573 a(A) p Fh 1854 573 a(2) p 1940 573 a(A) p Fl 2013 587 a(0) p Fp 2052 573 a(.) p 2118 573 a(Then,) p 2381 573 a(b) m(y) p 2507 573 a(Lemma) p 2831 573 a(2.4,) p Fn 1100 789 a(U) p Fp 1172 789 a(\() p Fn(t) p Fp(\)) p Fn(A') p Fh 1428 789 a(\000) p Fn 1524 789 a(A') p Fp 448 789 a(\(2.17\)) 1428 974 y(=) p Fi 1524 859 a(Z) p Fj 1607 885 a(t) p Fl 1571 1048 a(0) p Fn 1652 974 a(ds) p 1767 974 a(e) p Fj 1809 937 a(isH) p Ff 1924 948 a(!) r(;) p Fd(E) p Fn 2030 974 a(i) p Fp([) p Fn(H) p Fj 2162 988 a(!) r(;) p Fm(E) p Fn 2275 974 a(;) p 2315 974 a(A) p Fp(]) p Fn(e) p Fm 2450 937 a(\000) p Fj(isH) p Ff 2620 948 a(!) r(;) p Fd(E) p Fn 2726 974 a(') 448 1230 y @beginspecial @setspecial @endspecial Fp(as) p 561 1230 a(elemen) m(ts) p 933 1230 a(of) p Fn 1038 1230 a(l) p Fl 1067 1197 a(2) p Fp 1106 1230 a(\() p Fk(Z) p 1161 1230 a(Z) p Fj 1216 1194 a(d) p Fp 1257 1230 a(\).) p 1360 1230 a(W) p 1445 1230 a(e) p 1518 1230 a(let) p Fn 1650 1230 a(') p Fp 1736 1230 a(=) p Fn 1833 1230 a(\016) p Fj 1873 1244 a(y) p Fh 1942 1230 a(2) p 2029 1230 a(D) p Fp 2102 1230 a(\() p Fn(H) p Fj 2213 1244 a(!) r(;) p Fm(E) p Fp 2325 1230 a(\),) p 2417 1230 a(and) p 2595 1230 a(tak) m(e) p 2793 1230 a(the) p Fn 2950 1230 a(l) p Fl 2979 1197 a(2) p Fp 3019 1230 a(\() p Fk(Z) p 3074 1230 a(Z) p Fj 3129 1194 a(d) p Fp 3169 1230 a(\)-inner) 448 1355 y(pro) s(duct) p 789 1355 a(of) p 893 1355 a(\(2.17\)) p 1156 1355 a(with) p Fn 1363 1355 a(\016) p Fj 1403 1369 a(x) p Fp 1477 1355 a(\() p Fn(x) p Fp(,) p Fn 1620 1355 a(y) p Fh 1693 1355 a(2) p Fk 1779 1355 a(Z) p 1799 1355 a(Z) p Fj 1854 1318 a(d) p Fp 1894 1355 a(\).) p 1995 1355 a(Then,) p 2258 1355 a(w) m(e) p 2392 1355 a(ha) m(v) m(e) p Fn 1070 1607 a(U) p Fp 1142 1607 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fh 1334 1607 a(\000) p Fn 1425 1607 a(A) p Fp 1518 1607 a(=) p Fi 1614 1492 a(Z) p Fj 1697 1518 a(t) p Fl 1660 1681 a(0) p Fn 1742 1607 a(ds) p 1857 1607 a(e) p Fj 1899 1569 a(isH) p Ff 2014 1580 a(!) r(;) p Fd(E) p Fn 2119 1607 a(i) p Fp([) p Fn(H) p Fj 2251 1621 a(!) r(;) p Fm(E) p Fn 2365 1607 a(;) p 2405 1607 a(A) p Fp(]) p Fn(e) p Fm 2540 1569 a(\000) p Fj(isH) p Ff 2710 1580 a(!) r(;) p Fd(E) p Fp 448 1607 a(\(2.18\)) 448 1856 y @beginspecial @setspecial @endspecial(as) p 566 1856 a(elemen) m(ts) p 944 1856 a(of) p Fh 1054 1856 a(L) p Fl 1117 1823 a(2) p Fp 1156 1856 a(,) p 1219 1856 a(for) p 1365 1856 a(LHS) p 1577 1856 a(of) p 1687 1856 a(\(2.18\)) p 1955 1856 a(b) s(elongs) p 2288 1856 a(to) p Fh 2405 1856 a(L) p Fl 2468 1823 a(2) p Fp 2507 1856 a(.) p 2592 1856 a(W) p 2677 1856 a(e) p 2755 1856 a(will) p 2932 1856 a(sho) m(w) p Fn 3164 1856 a(U) p Fp 3236 1856 a(\() p Fn(t) p Fp(\)) p 3376 1856 a(is) 448 1980 y(strongly) p 800 1980 a(con) m(tin) m(uous) p 1255 1980 a(on) p Fh 1381 1980 a(L) p Fl 1444 1948 a(2) p Fp 1484 1980 a(.) p 1549 1980 a(Let) p Fn 1712 1980 a(A) p Fh 1806 1980 a(2) p 1891 1980 a(A) p Fl 1964 1994 a(0) p Fp 2003 1980 a(.) p 2069 1980 a(By) p 2212 1980 a(\(2.18\),) p Fn 724 2196 a(<) p Fp 820 2196 a(\() p Fn 856 2196 a(U) p Fp 928 2196 a(\() p Fn(t) p Fp(\)) p Fh(\000) p Fn(I) p Fp 1149 2196 a(\)) p Fn(A;) p Fp 1292 2196 a(\() p Fn(U) p Fp 1399 2196 a(\() p Fn(t) p Fp(\)) p Fh 1524 2196 a(\000) p Fn 1615 2196 a(I) p Fp 1662 2196 a(\)) p Fn(A) p 1791 2196 a(>) p Fm 1862 2216 a(L) p Fc 1911 2197 a(2) p Fp 448 2196 a(\(2.19\)) 908 2382 y(=) p Fn 1031 2382 a(<) p Fi 1127 2267 a(Z) p Fj 1210 2293 a(t) p Fl 1173 2455 a(0) p Fn 1255 2382 a(ds) p 1370 2382 a(e) p Fj 1412 2344 a(isH) p Ff 1527 2355 a(!) r(;) p Fd(E) p Fn 1633 2382 a(i) p Fp([) p Fn(H) p Fj 1765 2396 a(!) r(;) p Fm(E) p Fn 1878 2382 a(;) p 1918 2382 a(A) p Fp(]) p Fn(e) p Fm 2053 2344 a(\000) p Fj(isH) p Ff 2223 2355 a(!) r(;) p Fd(E) p Fn 2329 2382 a(;) p Fi 1395 2503 a(Z) p Fj 1478 2530 a(t) p Fl 1441 2692 a(0) p Fn 1523 2618 a(du) p 1647 2618 a(e) p Fj 1689 2581 a(iuH) p Ff 1812 2592 a(!) r(;) p Fd(E) p Fn 1918 2618 a(i) p Fp([) p Fn(H) p Fj 2050 2632 a(!) r(;) p Fm(E) p Fn 2163 2618 a(;) p 2203 2618 a(A) p Fp(]) p Fn(e) p Fm 2338 2581 a(\000) p Fj(iuH) p Ff 2516 2592 a(!) r(;) p Fd(E) p Fn 2648 2618 a(>) p Fm 2719 2638 a(L) p Fc 2768 2619 a(2) p Fp 908 2855 a(=) p Fi 1031 2740 a(Z) p Fl 1077 2928 a(\012) p Fn 1148 2855 a(d) p Fe(P) p Fi 1313 2774 a(X) p Fj 1282 2972 a(x) p Fm(2) p Fg(Z) p 1385 2972 a(Z) p Ff 1427 2947 a(d) p Fi 1479 2740 a(Z) p Fj 1562 2766 a(t) p Fl 1525 2928 a(0) p Fn 1606 2855 a(ds) p Fi 1711 2740 a(Z) p Fj 1795 2766 a(t) p Fl 1758 2928 a(0) p Fn 1839 2855 a(du) p 1964 2777 582 4 v Fp 1964 2855 a(\() p Fn(V) p Fp 2073 2855 a(\() p Fn(s) p Fp(\)\)\() p Fn(!) p Fp 2332 2855 a(;) p Fn 2372 2855 a(x;) p Fp 2464 2855 a(0\)) q(\() p Fn(V) p Fp 2654 2855 a(\() p Fn(u) p Fp(\)\)\() p Fn(!) p Fp 2922 2855 a(;) p Fn 2962 2855 a(x;) p Fp 3054 2855 a(0\)) p Fn(;) 448 3148 y @beginspecial @setspecial @endspecial Fp(where) 873 3272 y(\() p Fn(V) p Fp 982 3272 a(\() p Fn(s) p Fp(\)\)\() p Fn(!) p Fp 1241 3272 a(;) p Fn 1281 3272 a(x;) p 1373 3272 a(y) p Fp 1421 3272 a(\)) p 1482 3272 a(:=) p Fi 1603 3178 a(\020) p Fn 1653 3272 a(e) p Fj 1695 3235 a(isH) p Ff 1810 3246 a(!) r(;) p Fd(E) p Fn 1915 3272 a(i) p Fp([) p Fn(H) p Fj 2047 3286 a(!) r(;) p Fm(E) p Fn 2160 3272 a(;) p 2200 3272 a(A) p Fp(]) p Fn(e) p Fm 2335 3235 a(\000) p Fj(isH) p Ff 2505 3246 a(!) r(;) p Fd(E) p Fi 2611 3178 a(\021) p Fp 2661 3272 a(\() p Fn(!) p Fp 2771 3272 a(;) p Fn 2811 3272 a(x;) p 2903 3272 a(y) p Fp 2951 3272 a(\)) p Fn(:) 448 3462 y @beginspecial @setspecial @endspecial Fp(By) p 595 3462 a(Prop) s(osition) p 1088 3462 a(2.5,) p Fn 1264 3462 a(V) p Fp 1338 3462 a(\() p Fn(s) p Fp(\)) p 1485 3462 a(is) p 1580 3462 a(b) s(ounded) p 1955 3462 a(in) p Fh 2065 3462 a(L) p Fl 2128 3429 a(2) p Fp 2201 3462 a(uniformly) p 2620 3462 a(w.r.t.) p Fn 2884 3462 a(s) p Fh 2958 3462 a(2) p Fp 3050 3462 a(I) p 3068 3462 a(R.) p 3212 3462 a(Th) m(us,) 448 3587 y(w) m(e) p 582 3587 a(use) p 739 3587 a(F) p 790 3587 a(ubini's) p 1084 3587 a(theorem) 731 3803 y(the) p 888 3803 a(RHS) p 1104 3803 a(of) p 1207 3803 a(\(2.19\)) 913 3988 y(=) p Fi 1009 3873 a(Z) p Fj 1092 3899 a(t) p Fl 1055 4062 a(0) p Fn 1137 3988 a(ds) p Fi 1267 3873 a(Z) p Fj 1350 3899 a(t) p Fl 1313 4062 a(0) p Fn 1395 3988 a(du) p Fi 1535 3873 a(Z) p Fl 1581 4062 a(\012) p Fn 1651 3988 a(d) p Fe(P) p Fi 1816 3907 a(X) p Fj 1785 4106 a(x) p Fm(2) p Fg(Z) p 1888 4106 a(Z) p Ff 1931 4080 a(d) p 1982 3910 V Fp 1982 3988 a(\() p Fn(V) p Fp 2091 3988 a(\() p Fn(s) p Fp(\)\)\() p Fn(!) p Fp 2350 3988 a(;) p Fn 2390 3988 a(x;) p Fp 2482 3988 a(0\)) q(\() p Fn(V) p Fp 2672 3988 a(\() p Fn(u) p Fp(\)\)\() p Fn(!) p Fp 2940 3988 a(;) p Fn 2980 3988 a(x;) p Fp 3072 3988 a(0\)) 913 4281 y(=) p Fi 1009 4166 a(Z) p Fj 1092 4192 a(t) p Fl 1055 4355 a(0) p Fn 1137 4281 a(ds) p Fi 1267 4166 a(Z) p Fj 1350 4192 a(t) p Fl 1313 4355 a(0) p Fn 1395 4281 a(du) p 1545 4281 a(<) p 1641 4281 a(V) p Fp 1714 4281 a(\() p Fn(s) p Fp(\)) p Fn(;) p 1867 4281 a(V) p Fp 1941 4281 a(\() p Fn(u) p Fp(\)) p Fn 2089 4281 a(>) p Fm 2160 4301 a(L) p Fc 2209 4282 a(2) p Fn 2272 4281 a(:) 448 4530 y @beginspecial @setspecial @endspecial Fp(Since) p Fh 682 4530 a(A) p Fl 755 4544 a(0) p Fp 820 4530 a(is) p 907 4530 a(dense) p 1151 4530 a(in) p Fh 1253 4530 a(L) p Fl 1316 4497 a(2) p Fp 1355 4530 a(,) p 1408 4530 a(w) m(e) p 1537 4530 a(conclude) p 1907 4530 a(that) p Fn 2100 4530 a(U) p Fp 2172 4530 a(\() p Fn(t) p Fp(\)) p 2302 4530 a(is) p 2389 4530 a(strongly) p 2737 4530 a(con) m(tin) m(uous) p 3188 4530 a(on) p Fh 3310 4530 a(L) p Fl 3373 4497 a(2) p Fp 3412 4530 a(.) 448 4655 y(By) p 591 4655 a(\(2.18\),) p Fn 1205 4815 a(U) p Fp 1277 4815 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fh 1469 4815 a(\000) p Fn 1560 4815 a(A) p Fp 1653 4815 a(=) p Fi 1749 4700 a(Z) p Fj 1832 4727 a(t) p Fl 1795 4889 a(0) p Fn 1877 4815 a(ds) p 1992 4815 a(U) p Fp 2064 4815 a(\() p Fn(s) p Fp(\)) p Fi 2177 4721 a(\020) p Fn 2227 4815 a(i) p Fp([) p Fn(H) p Fj 2359 4829 a(!) r(;) p Fm(E) p Fn 2472 4815 a(;) p 2512 4815 a(A) p Fp(]) p Fi 2605 4721 a(\021) p Fn 2655 4815 a(:) p Fp 1897 5225 a(19) p eop %%Page: 20 20 20 19 bop 448 573 a @beginspecial @setspecial @endspecial Fp(If) p Fn 541 573 a(A) p Fh 638 573 a(2) p 727 573 a(A) p Fl 800 587 a(0) p Fp 839 573 a(,) p 897 573 a(then) p Fn 1106 573 a(i) p Fp([) p Fn(H) p Fj 1238 587 a(!) r(;) p Fm(E) p Fn 1351 573 a(;) p 1391 573 a(A) p Fp(]) p Fh 1514 573 a(2) p 1603 573 a(L) p Fl 1666 540 a(2) p Fp 1737 573 a(so) p 1851 573 a(that) p 2050 573 a(the) p 2208 573 a(in) m(tegrand) p 2617 573 a(in) p 2725 573 a(RHS) p 2943 573 a(in) p 3051 573 a(the) p 3210 573 a(ab) s(o) m(v) m(e) 448 697 y(expression) p 891 697 a(is) p 986 697 a(con) m(tin) m(uous) p 1445 697 a(in) p Fh 1556 697 a(L) p Fl 1619 664 a(2) p Fp 1692 697 a(w.r.t.) p Fn 1958 697 a(s) p Fh 2032 697 a(2) p Fp 2125 697 a(I) p 2143 697 a(R.) p 2288 697 a(Hence,) p 2589 697 a(for) p Fn 2732 697 a(A) p Fh 2832 697 a(2) p 2925 697 a(A) p Fl 2998 711 a(0) p Fp 3037 697 a(,) p Fn 3098 697 a(U) p Fp 3170 697 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fp 3376 697 a(is) 448 822 y(di\013eren) m(tiable,) p 1019 822 a(and) p 1196 822 a(w) m(e) p 1330 822 a(ha) m(v) m(e) p Fn 1397 987 a(d) p 1381 1028 81 4 v 1381 1111 a(dt) 1471 1049 y(U) p Fp 1543 1049 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fp 1740 1049 a(=) p Fn 1836 1049 a(U) p Fp 1908 1049 a(\() p Fn(t) p Fp(\)) p Fi 2011 955 a(\020) p Fn 2061 1049 a(i) p Fp([) p Fn(H) p Fj 2193 1063 a(!) r(;) p Fm(E) p Fn 2306 1049 a(;) p 2346 1049 a(A) p Fp(]) p Fi 2439 955 a(\021) p Fn 2489 1049 a(:) 448 1250 y @beginspecial @setspecial @endspecial Fp(By) p 591 1250 a(Lemma) p 915 1250 a(2.4,) p 1087 1250 a(it) p 1178 1250 a(is) p 1270 1250 a(easy) p 1470 1250 a(to) p 1581 1250 a(see) p Fn 810 1451 a(i) p Fh(L) p Fj 904 1465 a(H) p Ff 962 1476 a(!) r(;) p Fd(E) p Fi 1067 1357 a(\020) p Fn 1117 1451 a(U) p Fp 1189 1451 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fi 1360 1357 a(\021) p Fp 1410 1451 a(\() p Fn(!) p Fp 1520 1451 a(;) p Fn 1560 1451 a(x;) p 1652 1451 a(y) p Fp 1700 1451 a(\)) p 1761 1451 a(=) p Fn 1857 1451 a(U) p Fp 1929 1451 a(\() p Fn(t) p Fp(\)) p Fi 2032 1357 a(\020) p Fn 2082 1451 a(i) p Fp([) p Fn(H) p Fj 2214 1465 a(!) r(;) p Fm(E) p Fn 2328 1451 a(;) p 2368 1451 a(A) p Fp(]) p Fi 2461 1357 a(\021) p Fp 2511 1451 a(\() p Fn(!) p Fp 2621 1451 a(;) p Fn 2661 1451 a(x;) p 2753 1451 a(y) p Fp 2801 1451 a(\)) p Fh 2863 1451 a(2) p 2948 1451 a(L) p Fl 3011 1413 a(2) p Fn 3051 1451 a(;) 448 1652 y @beginspecial @setspecial @endspecial Fp(for) p Fn 587 1652 a(A) p Fh 681 1652 a(2) p 767 1652 a(A) p Fl 840 1666 a(0) p Fp 879 1652 a(,) p 934 1652 a(and) p 1111 1652 a(hence,) p 1389 1652 a(w) m(e) p 1523 1652 a(ha) m(v) m(e) p Fn 1732 1652 a(U) p Fp 1804 1652 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fh 2001 1652 a(2) p 2087 1652 a(D) p Fp 2160 1652 a(\() p Fh(L) p Fj 2258 1666 a(H) p Ff 2316 1677 a(!) r(;) p Fd(E) p Fp 2421 1652 a(\),) p 2512 1652 a(and) p Fn 1213 1835 a(d) p 1196 1875 V 1196 1958 a(dt) 1286 1896 y(U) p Fp 1358 1896 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fp 1555 1896 a(=) p Fn 1651 1896 a(i) p Fh(L) p Fj 1745 1910 a(H) p Ff 1803 1921 a(!) r(;) p Fd(E) p Fi 1909 1802 a(\020) p Fn 1958 1896 a(U) p Fp 2030 1896 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fi 2201 1802 a(\021) p Fn 2251 1896 a(;) p 2383 1896 a(A) p Fh 2476 1896 a(2) p 2562 1896 a(A) p Fl 2635 1910 a(0) p Fn 2674 1896 a(:) 448 2106 y @beginspecial @setspecial @endspecial Fp(Therefore,) p 884 2106 a(b) m(y) p 1008 2106 a(uniqueness) p 1463 2106 a(of) p 1564 2106 a(solution) p 1906 2106 a(of) p 2007 2106 a(time-indep) s(enden) m(t) p 2727 2106 a(Sc) m(hr\177) p 2902 2106 a(odinger) p 3222 2106 a(equa-) 448 2231 y(tion,) p Fn 1352 2355 a(U) p Fp 1424 2355 a(\() p Fn(t) p Fp(\)) p Fn(A) p Fp 1621 2355 a(=) p Fn 1717 2355 a(e) p Fj 1759 2308 a(it) p Fm(L) p Ff 1857 2319 a(H) 1907 2336 y(!) r(;) p Fd(E) p Fn 2017 2355 a(A;) p 2216 2355 a(A) p Fh 2310 2355 a(2) p 2396 2355 a(A) p Fl 2469 2369 a(0) p Fn 2508 2355 a(;) 448 2526 y @beginspecial @setspecial @endspecial Fp(as) p 560 2526 a(desired.) p 904 2462 60 4 v 904 2551 4 89 v 960 2551 V 904 2554 60 4 v Fe 448 2827 a(Prop) s(osition) p 1014 2827 a(2.8) p 1193 2827 a @beginspecial @setspecial @endspecial Fo(F) p 1245 2827 a(or) p Fn 1362 2827 a(f) p Fp 1417 2827 a(\() p Fn(\025) p Fp(\)) p 1566 2827 a(=) p Fn 1662 2827 a(f) p Fj 1707 2842 a(\014) s(;\026) p Fp 1815 2827 a(\() p Fn(\025) p Fp(\)) p Fo(,) p 1999 2827 a(or) p Fn 2117 2827 a(\037) p Fl 2174 2845 a(\() p Fm(\0001) p Fj(;\026) p Fl(]) p Fp 2412 2827 a(\() p Fn(\025) p Fp(\)) p Fo(,) p Fh 1353 3028 a(T) p Fp 1426 3028 a(\() p Fn(f) p Fp 1516 3028 a(\() p Fn(H) p Fj 1627 3042 a(!) p Fp 1677 3028 a(\)) p Fn(@) p Fl 1760 3042 a(1) p Fn 1800 3028 a(H) p Fj 1876 3042 a(!) p Fp 1926 3028 a(\)) p 1986 3028 a(=) p 2082 3028 a(0) p Fn(;) p Fo 2261 3028 a(a.e.) p Fn 2447 3028 a(!) s(:) p Fp 448 3028 a(\(2.20\)) 448 3478 y @beginspecial @setspecial @endspecial Fo(Pr) p 543 3478 a(o) p 584 3478 a(of.) p Fp 728 3478 a(W) p 813 3478 a(e) p 885 3478 a(divide) p 1155 3478 a(the) p 1311 3478 a(pro) s(of) p 1549 3478 a(in) m(to) p 1733 3478 a(some) p 1961 3478 a(steps.) 589 3602 y @beginspecial @setspecial @endspecial Fo(Step) p 792 3602 a(1.) p Fp 906 3602 a(W) p 991 3602 a(e) p 1063 3602 a(will) p 1235 3602 a(sho) m(w) p Fh 1329 3803 a(T) p Fp 1402 3803 a(\() p Fn(e) p Fm 1479 3766 a(\000) p Fj(itH) p Ff 1641 3777 a(!) r(;) p Fd(E) p Fn 1747 3803 a(@) p Fl 1795 3817 a(1) p Fn 1835 3803 a(H) p Fj 1911 3817 a(!) p Fp 1961 3803 a(\)) p 2022 3803 a(=) p 2118 3803 a(0) p Fn(;) p Fp 2294 3803 a(a.e.) p Fn 2471 3803 a(!) s(:) p Fp 448 3803 a(\(2.21\)) 448 4004 y @beginspecial @setspecial @endspecial Fo(pr) p 527 4004 a(o) p 568 4004 a(of) p 677 4004 a(of) p 784 4004 a(\(2.21\)) 589 4129 y @beginspecial @setspecial @endspecial Fp(Let) p Fh 752 4129 a(r) p Fj 828 4143 a(n) p Fp 905 4129 a(b) s(e) p 1029 4129 a(a) p 1105 4129 a(b) s(ounded) p 1476 4129 a(op) s(erator) p 1843 4129 a(on) 1990 4106 y(~) p Fh 1969 4129 a(L) p Fl 2032 4096 a(2) p Fp 2101 4129 a(de\014ned) p 2415 4129 a(b) m(y) 955 4356 y(\() p Fh(r) p Fj 1066 4370 a(n) p Fn 1113 4356 a(a) p Fp(\)\() p Fn(!) s(;) p 1331 4356 a(x) p Fp(\)) p 1444 4356 a(:=) p Fi 1565 4237 a(\032) p Fn 1643 4299 a(x) p Fl 1695 4313 a(1) p Fn 1734 4299 a(a) p Fp(\() p Fn(!) s(;) p 1917 4299 a(x) p Fp(\)) p Fn(;) p Fp 2394 4299 a(\(if) p Fh 2512 4299 a(j) p Fn(x) p Fl 2589 4313 a(1) p Fh 2629 4299 a(j) p 2679 4299 a(\024) p Fn 2775 4299 a(n) p Fp(\),) 1643 4412 y(\(sgn) p Fn(x) p Fl 1862 4426 a(1) p Fp 1901 4412 a(\)) p Fn(n) p 2006 4412 a(a) p Fp(\() p Fn(!) s(;) p 2189 4412 a(x) p Fp(\)) p Fn(;) p Fp 2394 4412 a(\(otherwise\).) 448 4595 y @beginspecial @setspecial @endspecial(In) p Fh 569 4595 a(L) p Fl 632 4562 a(2) p Fp 671 4595 a(,) p Fh 735 4595 a(r) p Fj 811 4609 a(n) p Fp 894 4595 a(corresp) s(onds) p 1400 4595 a(to) p 1518 4595 a(the) p 1681 4595 a(follo) m(wing) p 2072 4595 a(op) s(erator) p 2445 4595 a(whic) m(h) p 2712 4595 a(w) m(e) p 2852 4595 a(also) p 3042 4595 a(denote) p 3341 4595 a(b) m(y) p Fh 448 4720 a(r) p Fj 524 4734 a(n) p Fp 571 4720 a(.) 613 4943 y(\() p Fh(r) p Fj 724 4957 a(n) p Fn 771 4943 a(A) p Fp(\)\() p Fn(!) p Fp 985 4943 a(;) p Fn 1025 4943 a(x;) p 1117 4943 a(y) p Fp 1165 4943 a(\)) p 1226 4943 a(=) p Fi 1322 4824 a(\032) p Fp 1400 4886 a(\() p Fn(x) p Fl 1487 4900 a(1) p Fh 1547 4886 a(\000) p Fn 1638 4886 a(y) p Fl 1683 4900 a(1) p Fp 1722 4886 a(\)) p Fn(A) p Fp(\() p Fn(!) p Fp 1936 4886 a(;) p Fn 1976 4886 a(x;) p 2068 4886 a(y) p Fp 2116 4886 a(\)) p Fn(;) p Fp 2540 4886 a(\(if) p Fh 2659 4886 a(j) p Fn(x) p Fl 2736 4900 a(1) p Fh 2795 4886 a(\000) p Fn 2886 4886 a(y) p Fl 2931 4900 a(1) p Fh 2970 4886 a(j) p 3021 4886 a(\024) p Fn 3117 4886 a(n) p Fp(\),) 1400 4999 y(\(sgn\() p Fn(x) p Fl 1654 5013 a(1) p Fh 1714 4999 a(\000) p Fn 1805 4999 a(y) p Fl 1850 5013 a(1) p Fp 1889 4999 a(\)\)) p Fn(n) p 2029 4999 a(A) p Fp(\() p Fn(!) p Fp 2208 4999 a(;) p Fn 2248 4999 a(x;) p 2340 4999 a(y) p Fp 2388 4999 a(\)) p Fn(;) p Fp 2540 4999 a(\(otherwise\).) 1897 5225 y(20) p eop %%Page: 21 21 21 20 bop Fn 448 573 a(e) p Fj 490 540 a(isH) p Ff 605 548 a(!) p Fh 654 573 a(r) p Fj 730 587 a(n) p Fp 777 573 a(\() p Fn(e) p Fm 854 540 a(\000) p Fj(isH) p Ff 1024 548 a(!) p Fp 1073 573 a(\)) p Fh 1134 573 a(2) p 1220 573 a(L) p Fl 1283 540 a(2) p Fp 1322 573 a(,) p 1377 573 a(and) p Fi 692 675 a(\020) p Fn 742 769 a(e) p Fj 784 732 a(isH) p Ff 899 740 a(!) p Fh 948 769 a(r) p Fj 1024 783 a(n) p Fp 1070 769 a(\() p Fn(e) p Fm 1147 732 a(\000) p Fj(isH) p Ff 1317 740 a(!) p Fp 1366 769 a(\)) p Fi 1401 675 a(\021) p Fp 1451 769 a(\() p Fn(!) p Fp 1562 769 a(;) p Fn 1602 769 a(x;) p 1694 769 a(y) p Fp 1742 769 a(\)) p 1803 769 a(=) p Fn(<) p 1970 769 a(\016) p Fj 2010 783 a(x) p Fn 2054 769 a(;) p 2094 769 a(e) p Fj 2136 732 a(isH) p Ff 2251 740 a(!) p Fh 2300 769 a(r) p Fj 2376 783 a(n) p Fp 2423 769 a(\() p Fn(e) p Fm 2500 732 a(\000) p Fj(isH) p Ff 2670 740 a(!) p Fp 2719 769 a(\)) p Fn(\016) p Fj 2794 783 a(y) p Fn 2861 769 a(>) p Fj 2932 798 a(l) p Fc 2954 779 a(2) p Fl 2989 798 a(\() p Fg(Z) p 3032 798 a(Z) p Ff 3075 773 a(d) p Fl 3111 798 a(\)) p Fn 3168 769 a(:) 448 966 y @beginspecial @setspecial @endspecial Fp(Since) p Fh 690 966 a(r) p Fj 766 980 a(n) p Fp 846 966 a(corresp) s(onds) p 1349 966 a(to) p 1464 966 a(a) p 1544 966 a(m) m(ultiplication) p 2131 966 a(op) s(erator) p 2501 966 a(b) m(y) p 2631 966 a(a) p 2711 966 a(b) s(ounded) p 3086 966 a(function,) 448 1091 y(and) p Fn 630 1091 a(\016) p Fj 670 1105 a(y) p Fh 746 1091 a(2) p 841 1091 a(D) p Fp 914 1091 a(\() p Fn(H) p Fj 1025 1105 a(!) p Fp 1075 1091 a(\),) p 1173 1091 a(for) p 1317 1091 a(an) m(y) p Fn 1494 1091 a(!) p Fh 1588 1091 a(2) p Fp 1683 1091 a(\012,) p 1811 1091 a(it) p 1907 1091 a(is) p 2004 1091 a(easy) p 2209 1091 a(to) p 2326 1091 a(sho) m(w) p 2557 1091 a(\() p Fh(r) p Fj 2668 1105 a(n) p Fp 2715 1091 a(\() p Fn(e) p Fm 2792 1058 a(\000) p Fj(isH) p Ff 2962 1069 a(!) r(;) p Fd(E) p Fp 3067 1091 a(\)) p Fn(\016) p Fj 3142 1105 a(y) p Fp 3184 1091 a(\)\() p Fn(x) p Fp(\)) p Fh 3377 1091 a(2) 448 1215 y(D) p Fp 521 1215 a(\() p Fn(H) p Fj 632 1229 a(!) p Fp 682 1215 a(\),) p 773 1215 a(for) p 912 1215 a(an) m(y) p Fn 1084 1215 a(!) p Fh 1169 1215 a(2) p Fp 1255 1215 a(\012.) p 1386 1215 a(Therefore,) p Fi 502 1318 a(\020) p Fn 552 1412 a(e) p Fj 594 1374 a(itH) p Ff 701 1382 a(!) p Fh 750 1412 a(r) p Fj 826 1426 a(n) p Fp 873 1412 a(\() p Fn(e) p Fm 950 1374 a(\000) p Fj(itH) p Ff 1112 1382 a(!) p Fp 1162 1412 a(\)) p Fi 1197 1318 a(\021) p Fp 1247 1412 a(\() p Fn(!) p Fp 1357 1412 a(;) p Fn 1397 1412 a(x;) p 1489 1412 a(y) p Fp 1537 1412 a(\)) 616 1626 y(=) p Fn 750 1626 a(i) p Fi 796 1511 a(Z) p Fj 880 1538 a(t) p Fl 843 1700 a(0) p Fn 925 1626 a(ds) p 1065 1626 a(<) p 1161 1626 a(\016) p Fj 1201 1640 a(x) p Fn 1245 1626 a(;) p 1285 1626 a(e) p Fj 1327 1589 a(isH) p Ff 1442 1597 a(!) p Fi 1492 1532 a(n) p Fn 1547 1626 a(H) p Fj 1623 1640 a(!) p Fp 1673 1626 a(\() p Fh(r) p Fj 1784 1640 a(n) p Fp 1831 1626 a(\() p Fn(e) p Fm 1908 1589 a(\000) p Fj(isH) p Ff 2078 1597 a(!) p Fp 2127 1626 a(\)\)) p Fh 2218 1626 a(\000) p 2309 1626 a(r) p Fj 2385 1640 a(n) p Fp 2432 1626 a(\() p Fn(H) p Fj 2543 1640 a(!) p Fn 2593 1626 a(e) p Fm 2635 1589 a(\000) p Fj(isH) p Ff 2805 1597 a(!) p Fp 2854 1626 a(\)) p Fi 2889 1532 a(o) p Fn 2945 1626 a(\016) p Fj 2985 1640 a(y) p Fn 3052 1626 a(>) p Fj 3123 1655 a(l) p Fc 3145 1636 a(2) p Fl 3179 1655 a(\() p Fg(Z) p 3222 1655 a(Z) p Ff 3265 1630 a(d) p Fl 3301 1655 a(\)) p Fn 3358 1626 a(:) 448 1863 y @beginspecial @setspecial @endspecial Fp(Because) p 795 1863 a(b) s(oth) p 1008 1863 a(sides) p 1225 1863 a(in) p 1329 1863 a(the) p 1484 1863 a(ab) s(o) m(v) m(e) p 1740 1863 a(equalit) m(y) p 2085 1863 a(b) s(elong) p 2374 1863 a(to) p Fn 2484 1863 a(l) p Fl 2513 1830 a(2) p Fp 2552 1863 a(\() p Fk(Z) p 2607 1863 a(Z) p Fj 2662 1827 a(d) p Fp 2703 1863 a(\)) p 2767 1863 a(w.r.t.) p Fn 3019 1863 a(x) p Fp(,) p 3125 1863 a(w) m(e) p 3258 1863 a(ha) m(v) m(e) p Fh 787 2060 a(r) p Fj 863 2074 a(n) p Fp 909 2060 a(\() p Fn(e) p Fm 986 2022 a(\000) p Fj(itH) p Ff 1148 2030 a(!) p Fp 1198 2060 a(\)) p 448 2060 a(\(2.22\)) 878 2245 y(=) p Fn 974 2245 a(e) p Fm 1016 2208 a(\000) p Fj(itH) p Ff 1178 2216 a(!) p Fi 1242 2131 a(Z) p Fj 1325 2157 a(t) p Fl 1288 2319 a(0) p Fn 1370 2245 a(ds) p 1485 2245 a(e) p Fj 1527 2208 a(isH) p Ff 1642 2216 a(!) p Fi 1691 2151 a(n) p Fn 1747 2245 a(H) p Fj 1823 2259 a(!) p Fh 1873 2245 a(r) p Fj 1949 2259 a(n) p Fp 1995 2245 a(\() p Fn(e) p Fm 2072 2208 a(\000) p Fj(isH) p Ff 2242 2216 a(!) p Fp 2291 2245 a(\)) p Fh 2347 2245 a(\000) p 2438 2245 a(r) p Fj 2514 2259 a(n) p Fp 2561 2245 a(\() p Fn(H) p Fj 2672 2259 a(!) p Fn 2722 2245 a(e) p Fm 2764 2208 a(\000) p Fj(isH) p Ff 2934 2216 a(!) p Fp 2983 2245 a(\)) p Fi 3018 2151 a(o) p Fn 3073 2245 a(:) 448 2463 y @beginspecial @setspecial @endspecial Fp(W) p 533 2463 a(e) p 605 2463 a(tak) m(e) p 802 2463 a(the) p 958 2463 a(trace) p 1186 2463 a(p) s(er) p 1345 2463 a(v) m(olume) p 1658 2463 a(on) p 1785 2463 a(b) s(oth) p 1999 2463 a(sides.) p 2253 2463 a(By) p 2396 2463 a(Prop) s(osition) p 2885 2463 a(2.2,) p Fh 1368 2659 a(T) p Fp 1440 2659 a(\() p Fh(r) p Fj 1551 2673 a(n) p Fp 1598 2659 a(\() p Fn(e) p Fm 1675 2622 a(\000) p Fj(itH) p Ff 1837 2630 a(!) p Fp 1887 2659 a(\)\)) p 1983 2659 a(=) p 2079 2659 a(0) p Fn(;) p Fp 2256 2659 a(a.e.) p Fn 2433 2659 a(!) s(:) p Fp 448 2659 a(\(2.23\)) 448 2856 y @beginspecial @setspecial @endspecial(On) p 607 2856 a(the) p 770 2856 a(other) p 1014 2856 a(hand,) p 1275 2856 a(in) p 1388 2856 a(the) p 1551 2856 a(pro) s(of) p 1796 2856 a(of) p 1906 2856 a(Lemma) p 2237 2856 a(3.1) p 2391 2856 a(in) p 2503 2856 a(section) p 2814 2856 a(3,) p 2923 2856 a(w) m(e) p 3064 2856 a(will) p 3242 2856 a(sho) m(w) 448 2980 y(that,) 589 3105 y @beginspecial @setspecial @endspecial(\(1\)) p Fh 733 3105 a(L) p Fl 796 3072 a(2) p Fp 863 3105 a(norm) p 1097 3105 a(of) p Fi 1198 3011 a(n) p Fn 1253 3105 a(H) p Fj 1329 3119 a(!) p Fh 1379 3105 a(r) p Fj 1455 3119 a(n) p Fp 1502 3105 a(\() p Fn(e) p Fm 1579 3072 a(\000) p Fj(isH) p Ff 1749 3080 a(!) p Fp 1798 3105 a(\)) p Fh 1847 3105 a(\000) p 1932 3105 a(r) p Fj 2008 3119 a(n) p Fp 2056 3105 a(\() p Fn(H) p Fj 2167 3119 a(!) p Fn 2217 3105 a(e) p Fm 2259 3072 a(\000) p Fj(isH) p Ff 2429 3080 a(!) p Fp 2478 3105 a(\)) p Fi 2513 3011 a(o) p Fp 2596 3105 a(is) p 2685 3105 a(b) s(ounded) p 3053 3105 a(uniformly) 448 3229 y(in) p Fn 554 3229 a(s) p Fp 627 3229 a(\(3.5\).) 589 3354 y @beginspecial @setspecial @endspecial(\(2\)) p Fi 737 3260 a(n) p Fn 792 3354 a(H) p Fj 868 3368 a(!) p Fh 918 3354 a(r) p Fj 994 3368 a(n) p Fp 1041 3354 a(\() p Fn(e) p Fm 1118 3321 a(\000) p Fj(isH) p Ff 1288 3329 a(!) p Fp 1337 3354 a(\)) p Fh 1393 3354 a(\000) p 1485 3354 a(r) p Fj 1561 3368 a(n) p Fp 1607 3354 a(\() p Fn(H) p Fj 1718 3368 a(!) p Fn 1769 3354 a(e) p Fm 1811 3321 a(\000) p Fj(isH) p Ff 1981 3329 a(!) p Fp 2030 3354 a(\)) p Fi 2065 3260 a(o) p Fh 2147 3354 a(!) p 2265 3354 a(\000) p Fp(\() p Fn(@) p Fl 2419 3368 a(1) p Fn 2459 3354 a(H) p Fj 2535 3368 a(!) p Fp 2585 3354 a(\)) p Fn(e) p Fm 2662 3321 a(\000) p Fj(isH) p Ff 2832 3329 a(!) p Fp 2912 3354 a(in) p Fh 3019 3354 a(L) p Fl 3082 3321 a(2) p Fp 3152 3354 a(as) p Fn 3265 3354 a(n) p Fh 3346 3354 a(!) 448 3478 y(1) p Fp 570 3478 a(\(Remark) p 947 3478 a(3.1\).) 589 3603 y @beginspecial @setspecial @endspecial(By) p 732 3603 a(\(1\),) p 904 3603 a(w) m(e) p 1038 3603 a(can) p 1204 3603 a(use) p 1361 3603 a(F) p 1412 3603 a(ubini's) p 1707 3603 a(theorem) p 2060 3603 a(and) p 2237 3603 a(conclude) p 2611 3603 a(that) p Fh 807 3836 a(T) p Fi 914 3742 a(\020) p Fn 963 3836 a(e) p Fm 1005 3798 a(\000) p Fj(itH) p Ff 1167 3806 a(!) p Fi 1232 3721 a(Z) p Fj 1315 3747 a(t) p Fl 1278 3909 a(0) p Fn 1360 3836 a(ds) p 1475 3836 a(e) p Fj 1517 3798 a(isH) p Ff 1632 3806 a(!) p Fi 1681 3742 a(n) p Fn 1737 3836 a(H) p Fj 1813 3850 a(!) p Fh 1862 3836 a(r) p Fj 1938 3850 a(n) p Fp 1985 3836 a(\() p Fn(e) p Fm 2062 3798 a(\000) p Fj(isH) p Ff 2232 3806 a(!) p Fp 2281 3836 a(\)) p Fh 2337 3836 a(\000) p 2428 3836 a(r) p Fj 2504 3850 a(n) p Fp 2551 3836 a(\() p Fn(H) p Fj 2662 3850 a(!) p Fn 2712 3836 a(e) p Fm 2754 3798 a(\000) p Fj(isH) p Ff 2924 3806 a(!) p Fp 2973 3836 a(\)) p Fi 3008 3742 a(o\021) p Fp 448 3836 a(\(2.24\)) 808 4072 y(=) p Fi 914 3957 a(Z) p Fj 997 3983 a(t) p Fl 960 4146 a(0) p Fn 1042 4072 a(ds) p Fh 1157 4072 a(T) p Fi 1230 3978 a(\020) p Fn 1279 4072 a(e) p Fm 1321 4035 a(\000) p Fj(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fj(H) p Ff 1625 4043 a(!) p Fi 1675 3978 a(n) p Fn 1730 4072 a(H) p Fj 1806 4086 a(!) p Fh 1856 4072 a(r) p Fj 1932 4086 a(n) p Fp 1979 4072 a(\() p Fn(e) p Fm 2056 4035 a(\000) p Fj(isH) p Ff 2226 4043 a(!) p Fp 2275 4072 a(\)) p Fh 2331 4072 a(\000) p 2422 4072 a(r) p Fj 2498 4086 a(n) p Fp 2545 4072 a(\() p Fn(H) p Fj 2656 4086 a(!) p Fn 2706 4072 a(e) p Fm 2748 4035 a(\000) p Fj(isH) p Ff 2918 4043 a(!) p Fp 2967 4072 a(\)) p Fi 3002 3978 a(o\021) p Fh 798 4308 a(!) p 914 4308 a(\000) p Fi 1000 4193 a(Z) p Fj 1083 4220 a(t) p Fl 1046 4382 a(0) p Fn 1128 4308 a(ds) p Fh 1243 4308 a(T) p Fp 1315 4308 a(\() p Fn(e) p Fm 1392 4271 a(\000) p Fj(itH) p Ff 1554 4279 a(!) p Fp 1604 4308 a(\() p Fn(@) p Fl 1687 4322 a(1) p Fn 1727 4308 a(H) p Fj 1803 4322 a(!) p Fp 1853 4308 a(\)\)) p Fn(;) p Fp 2055 4308 a(as) p Fn 2167 4308 a(n) p Fh 2247 4308 a(!) p 2363 4308 a(1) p Fn(:) 448 4531 y @beginspecial @setspecial @endspecial Fp(In) p 563 4531 a(the) p 721 4531 a(last) p 895 4531 a(step,) p 1114 4531 a(w) m(e) p 1250 4531 a(used) p 1459 4531 a(\(2\)) p 1606 4531 a(ab) s(o) m(v) m(e,) p 1891 4531 a(and) p 2069 4531 a(Prop) s(osition) p 2560 4531 a(2.2.) p 2746 4531 a(By) p 2890 4531 a(\(2.22\),) p 3180 4531 a(\(2.23\),) 448 4655 y(and) p 625 4655 a(\(2.24\),) p 913 4655 a(w) m(e) p 1047 4655 a(ha) m(v) m(e) p 1256 4655 a(\(2.21\).) 589 4780 y @beginspecial @setspecial @endspecial Fo(Step) p 792 4780 a(2.) p Fp 906 4780 a(F) p 957 4780 a(or) p Fn 1069 4780 a(z) p Fh 1141 4780 a(2) p 1253 4776 4 56 v Fp 1227 4780 a(C) o(,) p 1348 4780 a(Im) p Fn 1487 4780 a(z) p Fh 1558 4780 a(6) p Fp(=) p 1654 4780 a(0,) p 1755 4780 a(w) m(e) p 1889 4780 a(will) p 2061 4780 a(sho) m(w) p Fh 1260 4976 a(T) p Fp 1333 4976 a(\(\() p Fn(H) p Fj 1479 4990 a(!) p Fh 1550 4976 a(\000) p Fn 1641 4976 a(z) p Fp 1687 4976 a(\)) p Fm 1722 4939 a(\000) p Fl(1) p Fn 1816 4976 a(@) p Fl 1864 4990 a(1) p Fn 1904 4976 a(H) p Fj 1980 4990 a(!) p Fp 2030 4976 a(\)) p 2091 4976 a(=) p 2187 4976 a(0) p Fn(;) p Fp 2363 4976 a(a.e.) p Fn 2540 4976 a(!) s(:) p Fp 448 4976 a(\(2.25\)) 1897 5225 y(21) p eop %%Page: 22 22 22 21 bop 448 573 a @beginspecial @setspecial @endspecial Fo(Pr) p 543 573 a(o) p 584 573 a(of) p 692 573 a(of) p 799 573 a(\(2.25\).) 589 697 y @beginspecial @setspecial @endspecial Fp(If) p Fn 680 697 a(z) p Fp 752 697 a(=) p Fn 848 697 a(a) p Fp 916 697 a(+) p Fn 1007 697 a(i\025) p Fp(,) p 1147 697 a(for) p Fn 1286 697 a(\025) p 1364 697 a(>) p Fp 1460 697 a(0,) p Fh 729 911 a(T) p Fp 826 911 a(\(\() p Fn(H) p Fj 972 925 a(!) p Fh 1042 911 a(\000) p Fn 1133 911 a(a) p Fh 1202 911 a(\000) p Fn 1293 911 a(i\025) p Fp(\)) p Fm 1412 874 a(\000) p Fl(1) p Fn 1507 911 a(@) p Fl 1555 925 a(1) p Fn 1594 911 a(H) p Fj 1670 925 a(!) p Fp 1720 911 a(\)) p 448 911 a(\(2.26\)) 730 1085 y(=) p Fn 826 1085 a(i) p Fi 872 970 a(Z) p Fl 918 1158 a(\012) p Fn 988 1085 a(d) p Fe(P) p Fi 1153 1004 a(X) p Fj 1122 1202 a(x) p Fm(2) p Fg(Z) p 1225 1202 a(Z) p Ff 1268 1177 a(d) p Fi 1319 970 a(Z) p Fm 1402 996 a(1) p Fl 1366 1158 a(0) p Fn 1492 1085 a(dt) p 1598 1085 a(e) p Fm 1640 1047 a(\000) p Fj(\025t) p Fn 1766 1085 a(e) p Fj 1808 1047 a(ita) p Fp 1899 1085 a(\() p Fn(e) p Fm 1976 1047 a(\000) p Fj(itH) p Ff 2138 1055 a(!) p Fp 2188 1085 a(\)\() p Fn(!) p Fp 2334 1085 a(;) p 2374 1085 a(0) p Fn(;) p 2459 1085 a(x) p Fp(\)\() p Fn(@) p Fl 2629 1099 a(1) p Fn 2671 1085 a(H) p Fj 2747 1099 a(!) p Fp 2797 1085 a(\)\() p Fn(!) p Fp 2942 1085 a(;) p Fn 2982 1085 a(x;) p Fp 3074 1085 a(0\)) p Fn(:) 448 1391 y @beginspecial @setspecial @endspecial Fp(Since) p Fn 685 1391 a(e) p Fm 727 1358 a(\000) p Fj(itH) p Ff 889 1366 a(!) p Fh 963 1391 a(2) p 1049 1391 a(A) p Fp 1151 1391 a(and) p Fn 1327 1391 a(@) p Fl 1375 1405 a(1) p Fn 1414 1391 a(H) p Fj 1490 1405 a(!) p Fh 1565 1391 a(2) p 1651 1391 a(A) p Fl 1724 1405 a(0) p Fp 1763 1391 a(,) p 1818 1391 a(w) m(e) p 1951 1391 a(can) p 2116 1391 a(use) p 2272 1391 a(F) p 2323 1391 a(ubini's) p 2616 1391 a(theorem) p 2969 1391 a(to) p 3079 1391 a(exc) m(hange) p Fi 448 1447 a(R) p Fl 488 1543 a(\012) p Fn 558 1516 a(d) p Fe(P) p Fi 691 1451 a(P) p Fj 779 1545 a(x) p Fm(2) p Fg(Z) p 882 1545 a(Z) p Ff 925 1519 a(d) p Fp 996 1516 a(with) p Fi 1203 1447 a(R) p Fm 1258 1473 a(1) p Fl 1242 1543 a(0) p Fn 1348 1516 a(dt) p Fp(.) 988 1764 y(RHS) p 1204 1764 a(of) p 1307 1764 a(\(2.26\)) p 1565 1764 a(=) p Fn 1661 1764 a(i) p Fi 1707 1649 a(Z) p Fm 1790 1675 a(1) p Fl 1753 1838 a(0) p Fn 1880 1764 a(dt) p 1986 1764 a(e) p Fm 2028 1726 a(\000) p Fj(\025t) p Fn 2154 1764 a(e) p Fj 2196 1726 a(ita) p Fh 2287 1764 a(T) p Fp 2360 1764 a(\() p Fn(e) p Fm 2437 1726 a(\000) p Fj(itH) p Ff 2599 1734 a(!) p Fn 2649 1764 a(@) p Fl 2697 1778 a(1) p Fn 2736 1764 a(H) p Fj 2812 1778 a(!) p Fp 2862 1764 a(\)) 1565 1929 y(=) p 1661 1929 a(0) p Fn(:) 448 2143 y @beginspecial @setspecial @endspecial Fp(The) p 635 2143 a(pro) s(of) p 873 2143 a(of) p 976 2143 a(\(2.25\)) p 1239 2143 a(for) p Fn 1378 2143 a(\025) p 1456 2143 a(<) p Fp 1552 2143 a(0) p 1628 2143 a(is) p 1720 2143 a(similar.) 589 2268 y @beginspecial @setspecial @endspecial Fo(Step) p 795 2268 a(3.) p Fp 922 2268 a(\(completion\)) p 1461 2268 a(W) p 1546 2268 a(e) p 1622 2268 a(use) p 1783 2268 a(the) p 1944 2268 a(follo) m(wing) p 2332 2268 a(form) m(ula) p 2669 2268 a(whic) m(h) p 2933 2268 a(is) p 3029 2268 a(norm) p 3270 2268 a(con-) 448 2392 y(v) m(ergen) m(t.) p Fn 1028 2539 a(f) p Fj 1073 2554 a(\014) s(;\026) p Fp 1181 2539 a(\() p Fn(H) p Fj 1292 2553 a(!) p Fp 1343 2539 a(\)) p 1403 2539 a(=) 1552 2477 y(1) p 1509 2517 132 4 v 1509 2601 a(2) p Fn(\031) s(i) p Fi 1666 2424 a(Z) p 1733 2609 4 37 v Fl 1712 2612 a(C) p Fp 1767 2539 a(\() p Fn(@) p Fl 1854 2553 a(\026) p Fj 1850 2553 a(z) p Fp 1910 2515 a(~) p Fn 1891 2539 a(f) p Fj 1936 2554 a(\014) s(;\026) p Fp 2045 2539 a(\() p Fn(z) p Fp 2126 2539 a(\)\)\() p Fn(H) p Fj 2307 2553 a(!) p Fh 2378 2539 a(\000) p Fn 2469 2539 a(z) p Fp 2515 2539 a(\)) p Fm 2550 2501 a(\000) p Fl(1) p Fn 2645 2539 a(dz) t(d) p Fp 2790 2539 a(\026) p Fn 2785 2539 a(z) p 2833 2539 a(;) p Fp 448 2539 a(\(2.27\)) 448 2758 y @beginspecial @setspecial @endspecial(where) 737 2734 y(~) p Fn 718 2758 a(f) p Fj 763 2773 a(\014) s(;\026) p Fp 871 2758 a(\() p Fn(z) p Fp 952 2758 a(\)) p 1025 2758 a(is) p 1123 2758 a(the) p 1286 2758 a(almost) p 1585 2758 a(analytic) p 1938 2758 a(con) m(tin) m(uation) p 2469 2758 a(of) p Fn 2579 2758 a(f) p Fj 2624 2773 a(\014) s(;\026) p Fp 2733 2758 a(,) p 2796 2758 a(\() p Fn(@) p Fl 2883 2772 a(\026) p Fj 2879 2772 a(z) p Fn 2920 2758 a(f) p Fp 2975 2758 a(\)\() p Fn(x) p Fp 3121 2758 a(+) p Fn 3216 2758 a(iy) p Fp 3295 2758 a(\)) p 3366 2758 a(=) p Fl 458 2847 a(1) p 458 2862 36 4 v 458 2914 a(2) p Fp 504 2883 a(\() p Fn(@) p Fj 587 2897 a(x) p Fn 631 2883 a(f) p Fp 706 2883 a(+) p Fn 796 2883 a(i@) p Fj 875 2897 a(y) p Fn 917 2883 a(f) p Fp 972 2883 a(\)\() p Fn(x) p Fp 1115 2883 a(+) p Fn 1205 2883 a(iy) p Fp 1284 2883 a(\),) p 1376 2883 a(for) p Fn 1515 2883 a(z) p Fp 1586 2883 a(=) p Fn 1682 2883 a(x) p Fp 1754 2883 a(+) p Fn 1845 2883 a(iy) p Fp 1955 2883 a(\([11) q(]\).) p 2232 2883 a(Then,) p 2495 2883 a(b) m(y) p 2621 2883 a(\(2.25\),) p Fh 1309 3097 a(T) p Fp 1382 3097 a(\() p Fn(f) p Fj 1462 3112 a(\014) s(;\026) p Fp 1571 3097 a(\() p Fn(H) p Fj 1682 3111 a(!) p Fp 1732 3097 a(\)) p Fn(@) p Fl 1815 3111 a(1) p Fn 1855 3097 a(H) p Fj 1931 3111 a(!) p Fp 1981 3097 a(\)) p 2042 3097 a(=) p 2138 3097 a(0) p Fn(;) p Fp 2314 3097 a(a.e.) p Fn 2491 3097 a(!) s(;) 448 3311 y @beginspecial @setspecial @endspecial Fp(and) p 631 3311 a(th) m(us,) p 863 3311 a(w) m(e) p 1003 3311 a(ha) m(v) m(e) p 1218 3311 a(\(2.20\)) p 1487 3311 a(for) p Fn 1632 3311 a(f) p Fp 1687 3311 a(\() p Fn(\025) p Fp(\)) p 1845 3311 a(=) p Fn 1951 3311 a(f) p Fj 1996 3326 a(\014) s(;\026) p Fp 2104 3311 a(\() p Fn(\025) p Fp(\).) p 2311 3311 a(Since) p Fn 2554 3311 a(f) p Fj 2599 3326 a(\014) s(;\026) p Fp 2708 3311 a(\() p Fn(\025) p Fp(\)) p Fh 2867 3311 a(!) p Fn 2993 3311 a(\037) p Fl 3050 3329 a(\() p Fm(\0001) p Fj(;\026) p Fl(]) p Fp 3288 3311 a(\() p Fn(\025) p Fp(\),) 448 3435 y(p) s(oin) m(t) m(wise) p 865 3435 a(if) p Fn 962 3435 a(\025) p Fh 1065 3435 a(6) p Fp(=) p Fn 1185 3435 a(\026) p Fp(,) p 1313 3435 a(as) p Fn 1439 3435 a(\014) p Fh 1544 3435 a(!) p 1684 3435 a(1) p Fp(,) p 1849 3435 a(and) p 2040 3435 a(the) p 2211 3435 a(in) m(tegrated) p 2657 3435 a(densit) m(y) p 2985 3435 a(of) p 3103 3435 a(states) p 3376 3435 a(is) 448 3560 y(con) m(tin) m(uous,) p Fh 811 3791 a(T) p Fi 884 3696 a(\020) p Fp 934 3791 a(\() p Fn(f) p Fj 1014 3806 a(\014) s(;\026) p Fp 1123 3791 a(\() p Fn(H) p Fj 1234 3805 a(!) p Fp 1284 3791 a(\)) p Fh 1340 3791 a(\000) p Fn 1431 3791 a(P) p Fj 1489 3805 a(\026) p Fp 1535 3791 a(\)) p Fl 1570 3753 a(2) p Fi 1610 3696 a(\021) p Fp 1685 3791 a(=) p Fi 1781 3676 a(Z) p Fl 1827 3864 a(I) p 1840 3864 a(R) p Fp 1897 3791 a(\() p Fn(f) p Fj 1977 3806 a(\014) s(;\026) p Fp 2086 3791 a(\() p Fn(\025) p Fp(\)) p Fh 2230 3791 a(\000) p Fn 2321 3791 a(\037) p Fl 2378 3809 a(\() p Fm(\0001) p Fj(;\026) p Fl(]) p Fp 2616 3791 a(\() p Fn(\025) p Fp(\)\)) p Fl 2774 3753 a(2) p Fn 2815 3791 a(d) p Fh(N) p Fp 2950 3791 a(\() p Fn(\025) p Fp(\)) p Fh 1781 3961 a(!) p Fp 1897 3961 a(0) p Fn(;) p Fp 2074 3961 a(as) p Fn 2186 3961 a(\014) p Fh 2267 3961 a(") p 2338 3961 a(1) p Fn(;) 448 4175 y @beginspecial @setspecial @endspecial Fp(where) p Fn 711 4175 a(d) p Fh(N) p Fp 846 4175 a(\() p Fn(\025) p Fp(\)) p 1001 4175 a(is) p 1092 4175 a(the) p 1249 4175 a(densit) m(y) p 1562 4175 a(of) p 1666 4175 a(states) p 1924 4175 a(measure.) p 2314 4175 a(By) p 2457 4175 a(Sc) m(h) m(w) m(arz) p 2808 4175 a(inequalit) m(y) p 3193 4175 a(,) 1191 4389 y(0) p 1262 4389 a(=) p Fh 1358 4389 a(T) p Fp 1431 4389 a(\() p Fn(f) p Fj 1511 4404 a(\014) s(;\026) p Fp 1620 4389 a(\() p Fn(H) p Fj 1731 4403 a(!) p Fp 1781 4389 a(\)) p Fn(@) p Fl 1864 4403 a(1) p Fn 1904 4389 a(H) p Fj 1980 4403 a(!) p Fp 2030 4389 a(\)) p Fh 2091 4389 a(!) p 2207 4389 a(T) p Fp 2279 4389 a(\() p Fn(P) p Fj 2372 4403 a(\026) p Fn 2420 4389 a(@) p Fl 2468 4403 a(1) p Fn 2507 4389 a(H) p Fj 2583 4403 a(!) p Fp 2633 4389 a(\)) p Fn(;) 448 4603 y @beginspecial @setspecial @endspecial Fp(as) p Fn 560 4603 a(\014) p Fh 641 4603 a(!) p 758 4603 a(1) p Fp(,) p 904 4603 a(and) p 1081 4603 a(w) m(e) p 1215 4603 a(obtain) p 1497 4603 a(\(2.20\)) p 1760 4603 a(for) p Fn 1899 4603 a(\037) p Fl 1956 4621 a(\() p Fm(\0001) p Fj(;\026) p Fl(]) p Fp 2195 4603 a(\() p Fn(\025) p Fp(\).) p 2384 4539 60 4 v 2384 4628 4 89 v 2440 4628 V 2384 4631 60 4 v Fe 448 4852 a(Remark) p 846 4852 a(2.5) p 1025 4852 a @beginspecial @setspecial @endspecial Fo(When) p 1286 4852 a(we) p 1420 4852 a(imp) p 1563 4852 a(ose) p 1720 4852 a(c) p 1757 4852 a(onstant) p 2082 4852 a(magnetic) p 2468 4852 a(\014eld,) p 2690 4852 a(the) p 2840 4852 a(analysis) p 3185 4852 a(in) p 3295 4852 a(this) 448 4976 y(p) p 489 4976 a(ap) p 576 4976 a(er) p 704 4976 a(go) p 787 4976 a(es) p 913 4976 a(thr) p 1022 4976 a(ough) p 1253 4976 a(with) p 1464 4976 a(suitable) p 1807 4976 a(mo) p 1922 4976 a(di\014c) p 2084 4976 a(ations) p 2371 4976 a(in) p 2496 4976 a(the) p 2660 4976 a(de\014nitions) p 3117 4976 a(of) p 3237 4976 a(some) p Fp 1897 5225 a(22) p eop %%Page: 23 23 23 22 bop Fo 448 573 a(notations) p 856 573 a(describ) p 1126 573 a(e) p 1163 573 a(d) p 1251 573 a(b) p 1288 573 a(elow.) p 1555 573 a(L) p 1607 573 a(et) p Fe 1720 573 a(B) p Fp 1834 573 a(:=) p Fh 1971 573 a(f) p Fn(B) p Fj 2085 587 a(ij) p Fh 2145 573 a(g) p Fl 2190 588 a(1) p Fm(\024) p Fj(i;j) p Fm 2357 588 a(\024) p Fj(d) p Fo 2493 573 a(b) p 2530 573 a(e) p Fn 2613 573 a(d) p Fh 2686 573 a(\002) p Fn 2783 573 a(d) p Fo 2871 573 a(antisymmetric) 448 697 y(matrix) p 752 697 a(whose) p 1028 697 a(c) p 1065 697 a(omp) p 1226 697 a(onents) p 1530 697 a(ar) p 1609 697 a(e) p 1696 697 a(given) p 1945 697 a(by) p Fn 2075 697 a(B) p Fj 2144 711 a(ij) p Fp 2251 697 a(=) p Fh 2368 697 a(\000) p Fn(B) p Fj 2508 711 a(ij) p Fh 2614 697 a(2) p Fp 2721 697 a(I) p 2739 697 a(R) p Fo(,) p 2881 697 a(if) p Fn 2981 697 a(i) p 3058 697 a(<) p 3175 697 a(j) p Fo 3217 697 a(,) p 3293 697 a(and) p Fp 448 822 a(0) p Fo 533 822 a(if) p Fn 628 822 a(i) p Fp 696 822 a(=) p Fn 804 822 a(j) p Fo 846 822 a(.) p Fn 937 822 a(B) p Fj 1006 836 a(ij) p Fo 1105 822 a(c) p 1142 822 a(orr) p 1259 822 a(esp) p 1379 822 a(onds) p 1602 822 a(to) p 1718 822 a(the) p 1876 822 a(magnetic) p 2270 822 a(\015ux) p 2454 822 a(p) p 2495 822 a(enetr) p 2693 822 a(ating) p 2931 822 a(plaquettes) p 3358 822 a(in) p Fp 448 946 a(\() p Fn(i;) p 554 946 a(j) p Fp 596 946 a(\)) p Fo(-planes.) 589 1071 y @beginspecial @setspecial @endspecial(\(1\)) p 744 1071 a(The) p 931 1071 a(tr) p 994 1071 a(anslation) p 1389 1071 a(op) p 1476 1071 a(er) p 1551 1071 a(ator) p Fn 1749 1071 a(U) p Fp 1821 1071 a(\() p Fn(a) p Fp(\)) p Fo 1973 1071 a(de\014ne) p 2200 1071 a(d) p 2281 1071 a(after) p 2500 1071 a(\(2.1\)) p 2729 1071 a(should) p 3012 1071 a(b) p 3049 1071 a(e) p 3125 1071 a(r) p 3158 1071 a(eplac) p 3352 1071 a(e) p 3389 1071 a(d) 448 1196 y(by) p 567 1196 a(the) p 718 1196 a(magnetic) p 1106 1196 a(tr) p 1169 1196 a(anslation) p 1562 1196 a(given) p 1799 1196 a(by) p Fp 957 1406 a(\() p Fn(U) p Fb 1054 1420 a(B) p Fp 1117 1406 a(\() p Fn(a) p Fp(\)) p Fn( ) p Fp 1297 1406 a(\)\() p Fn(x) p Fp(\)) p 1481 1406 a(:=) p Fn 1602 1406 a(e) p Ff 1658 1341 a(i) p 1655 1353 31 4 v Fc 1655 1395 a(2) p Fj 1695 1369 a() p Fc 1960 1395 a(I) p 1971 1395 a(R) p Ff 2015 1381 a(d) p Fn 2059 1406 a( ) p Fp 2121 1406 a(\() p Fn(x) p Fh 2229 1406 a(\000) p Fn 2320 1406 a(a) p Fp(\)) p Fn(;) p 2537 1406 a(x;) p 2629 1406 a(a) p Fh 2703 1406 a(2) p Fk 2788 1406 a(Z) p 2807 1406 a(Z) p Fj 2862 1369 a(d) p Fn 2903 1406 a(:) 589 1617 y @beginspecial @setspecial @endspecial Fo(\(2\)) p 743 1617 a(The) p 929 1617 a(de\014nition) p 1335 1617 a(of) p 1442 1617 a(\(CR\)) p 1680 1617 a(in) p 1792 1617 a(\(2.2\)) p 2019 1617 a(should) p 2301 1617 a(b) p 2338 1617 a(e) p 2412 1617 a(r) p 2445 1617 a(eplac) p 2639 1617 a(e) p 2676 1617 a(d) p 2757 1617 a(by) p Fn 624 1827 a(H) p Fp 707 1827 a(\() p Fn(!) p Fp 818 1827 a(;) p Fn 858 1827 a(x;) p 950 1827 a(y) p Fp 998 1827 a(\)) p 1059 1827 a(=) p Fn 1155 1827 a(e) p Ff 1211 1763 a(i) p 1207 1775 V Fc 1207 1816 a(2) p Fj 1247 1790 a() p Fc 1658 1816 a(I) p 1669 1816 a(R) p Ff 1714 1802 a(d) p Fn 1759 1827 a(H) p Fp 1842 1827 a(\() p Fn(T) p Fm 1943 1790 a(\000) p Fj(a) p Fn 2039 1827 a(!) p Fp 2114 1827 a(;) p Fn 2154 1827 a(x) p Fh 2227 1827 a(\000) p Fn 2318 1827 a(a;) p 2406 1827 a(y) p Fh 2474 1827 a(\000) p Fn 2565 1827 a(a) p Fp(\)) p Fn(;) p 2782 1827 a(x;) p 2874 1827 a(y) s(;) p 2962 1827 a(a) p Fh 3036 1827 a(2) p Fk 3122 1827 a(Z) p 3141 1827 a(Z) p Fj 3196 1790 a(d) p Fn 3236 1827 a(:) 589 2038 y @beginspecial @setspecial @endspecial Fo(\(3\)) p Fn 757 2038 a(\031) p Fm 812 2005 a(\000) p Fl(1) p Fp 956 2038 a(:) p Fh 1032 2038 a(L) p Fl 1095 2005 a(2) p Fh 1184 2038 a(!) p Fp 1347 2015 a(~) p Fh 1326 2038 a(L) p Fl 1389 2005 a(2) p Fo 1474 2038 a(in) p 1600 2038 a(Pr) p 1695 2038 a(op) p 1782 2038 a(osition) p 2097 2038 a(2.1,) p 2295 2038 a(and) p 2486 2038 a(the) p 2650 2038 a(pr) p 2729 2038 a(o) p 2770 2038 a(duct) p 2986 2038 a(of) p Fn 3107 2038 a(A) p Fo(,) p Fn 3253 2038 a(B) p Fh 3377 2038 a(2) 448 2162 y(L) p Fl 511 2129 a(2) p Fo 594 2162 a(r) p 627 2162 a(epr) p 748 2162 a(esente) p 987 2162 a(d) p 1078 2162 a(in) p Fp 1221 2139 a(~) p Fh 1200 2162 a(L) p Fl 1263 2129 a(2) p Fo 1345 2162 a(in) p 1467 2162 a(\(2.4\)) p 1706 2162 a(should) p 1997 2162 a(b) p 2034 2162 a(e) p 2119 2162 a(given) p 2367 2162 a(by) p 2496 2162 a(the) p 2658 2162 a(fol) p 2760 2162 a(lowing) p 3054 2162 a(quantities) 448 2287 y(r) p 481 2287 a(esp) p 601 2287 a(e) p 638 2287 a(ctively:) p Fp 878 2498 a(\() p Fn(\031) p Fm 968 2460 a(\000) p Fl(1) p Fn 1063 2498 a(a) p Fp(\)\() p Fn(!) p Fp 1257 2498 a(;) p Fn 1297 2498 a(x;) p 1389 2498 a(y) p Fp 1437 2498 a(\)) p 1498 2498 a(=) p Fn 1594 2498 a(e) p Ff 1650 2433 a(i) p 1646 2445 V Fc 1646 2486 a(2) p Fj 1686 2460 a() p Fc 1951 2486 a(I) p 1962 2486 a(R) p Ff 2006 2472 a(d) p Fn 2050 2498 a(a) p Fp(\() p Fn(T) p Fm 2199 2460 a(\000) p Fj(y) p Fn 2296 2498 a(!) p Fp 2371 2498 a(;) p Fn 2411 2498 a(x) p Fh 2483 2498 a(\000) p Fn 2574 2498 a(y) p Fp 2622 2498 a(\)) p Fn(;) 878 2647 y(\031) p Fp 933 2647 a(\() p Fn(AB) p Fp 1110 2647 a(\)\() p Fn(!) s(;) p 1280 2647 a(x) p Fp(\)) p 1394 2647 a(=) p Fi 1518 2566 a(X) p Fj 1490 2765 a(z) p Fm 1526 2765 a(2) p Fg(Z) p 1588 2765 a(Z) p Ff 1631 2739 a(d) p Fn 1682 2647 a(e) p Ff 1738 2582 a(i) p 1734 2594 V Fc 1734 2635 a(2) p Fj 1775 2609 a() p Fc 2039 2635 a(I) p 2050 2635 a(R) p Ff 2093 2621 a(d) p Fn 2137 2647 a(a) p Fp(\() p Fn(T) p Fm 2286 2609 a(\000) p Fj(z) p Fn 2381 2647 a(!) s(;) p 2481 2647 a(x) p Fh 2553 2647 a(\000) p Fn 2644 2647 a(z) p Fp 2690 2647 a(\)) p Fn(b) p Fp(\() p Fn(!) s(;) p 2899 2647 a(z) p Fp 2945 2647 a(\)) p Fn(:) p Fq 448 3157 a(3) p 650 3157 a(Pro) t(of) p 1021 3157 a(of) p 1174 3157 a(Theorem) p 1744 3157 a(1) 448 3372 y @beginspecial @setspecial @endspecial Fp(In) p 558 3372 a(this) p 730 3372 a(section,) p 1056 3372 a(w) m(e) p 1185 3372 a(pro) m(v) m(e) p 1426 3372 a(Theorem) p 1806 3372 a(1.) p 1915 3372 a(The) p 2098 3372 a(follo) m(wing) p 2477 3372 a(prop) s(osition) p 2951 3372 a(is) p 3038 3372 a(imp) s(ortan) m(t) 448 3496 y(to) p 559 3496 a(study) p Fh 810 3496 a(E) p 891 3496 a(#) p Fp 962 3496 a(0) p 1038 3496 a(limit.) p Fe 448 3691 a(Prop) s(osition) p 1014 3691 a(3.1) p 1193 3691 a @beginspecial @setspecial @endspecial Fo(L) p 1245 3691 a(et) p Fn 1349 3691 a(A) p Fh 1443 3691 a(2) p 1529 3691 a(D) p Fp 1602 3691 a(\() p Fn(@) p Fl 1685 3705 a(1) p Fp 1724 3691 a(\)) p Fo(,) p Fh 831 3923 a(D) p Fp 904 3923 a(\() p Fn(@) p Fl 987 3937 a(1) p Fp 1027 3923 a(\)) p 1087 3923 a(:=) p Fh 1208 3923 a(f) p Fn(A) p Fh 1347 3923 a(2) p 1433 3923 a(L) p Fl 1496 3886 a(2) p Fp 1586 3923 a(:) p Fi 1662 3808 a(Z) p Fl 1708 3997 a(\012) p Fn 1778 3923 a(d) p Fe(P) p Fi 1943 3842 a(X) p Fj 1912 4041 a(x) p Fm(2) p Fg(Z) p 2014 4041 a(Z) p Ff 2057 4015 a(d) p Fh 2108 3923 a(j) p Fn(x) p Fl 2185 3937 a(1) p Fh 2225 3923 a(j) p Fl 2250 3886 a(2) p Fh 2290 3923 a(j) p Fn(A) p Fp(\() p Fn(!) p Fp 2493 3923 a(;) p Fn 2533 3923 a(x;) p Fp 2625 3923 a(0\)) p Fh(j) p Fl 2730 3886 a(2) p Fn 2797 3923 a(<) p Fh 2893 3923 a(1g) p Fn(:) 448 4211 y @beginspecial @setspecial @endspecial Fo(Then,) p 713 4211 a(we) p 848 4211 a(have) p 1057 4211 a(the) p 1208 4211 a(fol) p 1310 4211 a(lowing) p 1594 4211 a(r) p 1627 4211 a(esolvent) p 1974 4211 a(e) p 2011 4211 a(quation.) p Fp 691 4421 a(\() p Fn(z) p Fh 793 4421 a(\000) p 884 4421 a(L) p Fj 947 4435 a(H) p Ff 1005 4446 a(!) r(;) p Fd(E) p Fp 1110 4421 a(\)) p Fm 1145 4384 a(\000) p Fl(1) p Fn 1239 4421 a(A) p Fh 1333 4421 a(\000) p Fp 1429 4421 a(\() p Fn(z) p Fh 1531 4421 a(\000) p 1621 4421 a(L) p Fj 1684 4435 a(H) p Ff 1742 4443 a(!) p Fp 1791 4421 a(\)) p Fm 1826 4384 a(\000) p Fl(1) p Fn 1921 4421 a(A) p Fp 448 4421 a(\(3.1\)) 1333 4571 y(=) p 1429 4571 a(\() p Fn(z) p Fh 1531 4571 a(\000) p 1621 4571 a(L) p Fj 1684 4585 a(H) p Ff 1742 4596 a(!) r(;) p Fd(E) p Fp 1847 4571 a(\)) p Fm 1882 4533 a(\000) p Fl(1) p Fh 1977 4571 a(E) p Fn 2033 4571 a(@) p Fl 2081 4585 a(1) p Fp 2121 4571 a(\() p Fn(z) p Fh 2223 4571 a(\000) p 2314 4571 a(L) p Fj 2377 4585 a(H) p Ff 2435 4593 a(!) p Fp 2483 4571 a(\)) p Fm 2518 4533 a(\000) p Fl(1) p Fn 2613 4571 a(A;) p Fo 2814 4571 a(Im) p Fn 2956 4571 a(z) p Fh 3028 4571 a(6) p Fp(=) p 3124 4571 a(0) p Fn(:) 589 4976 y @beginspecial @setspecial @endspecial Fp(Before) p 874 4976 a(w) m(e) p 1008 4976 a(pro) m(v) m(e) p 1253 4976 a(Prop) s(osition) p 1742 4976 a(3.1,) p 1914 4976 a(w) m(e) p 2048 4976 a(prepare) p 2377 4976 a(the) p 2533 4976 a(follo) m(wing) p 2917 4976 a(lemma.) 1897 5225 y(23) p eop %%Page: 24 24 24 23 bop Fe 448 573 a(Lemma) p 819 573 a(3.1) p 998 573 a @beginspecial @setspecial @endspecial Fo(\(1\)) p 1156 573 a(L) p 1208 573 a(et) p Fn 1317 573 a(C) p Fh 1421 573 a(2) p 1515 573 a(L) p Fl 1578 540 a(2) p Fo 1617 573 a(.) p 1700 573 a(Then,) p Fh 1970 573 a(L) p Fl 2033 540 a(2) p Fo 2072 573 a(-norm) p 2352 573 a(of) p Fp 2463 573 a([) p Fh(L) p Fj 2551 587 a(H) p Ff 2609 595 a(!) p Fn 2658 573 a(;) p Fh 2698 573 a(r) p Fj 2774 587 a(n) p Fp 2821 573 a(]) p Fn(C) p Fo 2955 573 a(which) p 3214 573 a(is) p 3316 573 a(de-) 448 697 y(\014ne) p 587 697 a(d) p 667 697 a(by) p Fp 1140 822 a([) p Fh(L) p Fj 1228 836 a(H) p Ff 1286 844 a(!) p Fn 1335 822 a(;) p Fh 1375 822 a(r) p Fj 1451 836 a(n) p Fp 1498 822 a(]) p Fn(C) p Fp 1620 822 a(:=) p 1741 822 a([) p Fn(H) p Fj 1842 836 a(!) p Fn 1893 822 a(;) p Fh 1933 822 a(r) p Fj 2009 836 a(n) p Fn 2056 822 a(C) p Fp 2128 822 a(]) p Fh 2173 822 a(\000) p 2264 822 a(r) p Fj 2340 836 a(n) p Fp 2386 822 a(\([) p Fn(H) p Fj 2522 836 a(!) p Fn 2573 822 a(;) p 2613 822 a(C) p Fp 2685 822 a(]\)) 448 1000 y @beginspecial @setspecial @endspecial Fo(is) p 540 1000 a(b) p 577 1000 a(ounde) p 806 1000 a(d) p 880 1000 a(uniformly) p 1288 1000 a(w.r.t.) p Fn 1541 1000 a(n) p Fo 1622 1000 a(\() p Fh(r) p Fj 1735 1014 a(n) p Fo 1808 1000 a(is) p 1900 1000 a(de\014ne) p 2127 1000 a(d) p 2200 1000 a(in) p 2306 1000 a(the) p 2451 1000 a(pr) p 2530 1000 a(o) p 2571 1000 a(of) p 2673 1000 a(of) p 2774 1000 a(Pr) p 2869 1000 a(op) p 2956 1000 a(osition) p 3251 1000 a(2.8\).) 589 1125 y @beginspecial @setspecial @endspecial(\(2\)) p Fn 743 1125 a(@) p Fl 791 1139 a(1) p Fp 830 1125 a(\() p Fn(z) p Fh 932 1125 a(\000) p 1023 1125 a(L) p Fj 1086 1139 a(H) p Ff 1144 1147 a(!) p Fp 1193 1125 a(\)) p Fm 1228 1092 a(\000) p Fl(1) p Fn 1323 1125 a(A) p Fh 1416 1125 a(2) p 1502 1125 a(L) p Fl 1565 1092 a(2) p Fo 1604 1125 a(,) p 1664 1125 a(if) p Fn 1753 1125 a(A) p Fh 1846 1125 a(2) p 1932 1125 a(D) p Fp 2005 1125 a(\() p Fn(@) p Fl 2088 1139 a(1) p Fp 2128 1125 a(\)) p Fo(,) p 2223 1125 a(Im) p Fn 2365 1125 a(z) p Fh 2437 1125 a(6) p Fp(=) p 2533 1125 a(0) p Fo(.) 589 1324 y @beginspecial @setspecial @endspecial(Pr) p 684 1324 a(o) p 725 1324 a(of) p 833 1324 a(of) p 940 1324 a(L) p 992 1324 a(emma) p 1262 1324 a(3.1) 589 1449 y @beginspecial @setspecial @endspecial Fp(\(1\)) p 736 1449 a(Let) p Fn 899 1449 a(c) p Fp 963 1449 a(:=) p Fn 1085 1449 a(\031) p Fp 1140 1449 a(\() p Fn(C) p Fp 1247 1449 a(\),) p Fn 1337 1449 a(h) p Fp 1415 1449 a(:=) p Fn 1536 1449 a(\031) p Fp 1591 1449 a(\() p Fn(H) p Fj 1702 1463 a(!) p Fp 1753 1449 a(\).) p 1854 1449 a(Then,) p Fn 2116 1449 a(h) p Fp(\() p Fn(!) s(;) p 2303 1449 a(x) p Fp(\)) p 2422 1449 a(is) p 2513 1449 a(giv) m(en) p 2751 1449 a(b) m(y) p Fn 1272 1752 a(h) p Fp(\() p Fn(!) s(;) p 1459 1752 a(x) p Fp(\)) p 1572 1752 a(=) p Fi 1668 1580 a(8) 1668 1655 y(<) 1668 1804 y(:) p Fp 1757 1639 a(1) p Fn(;) p Fp 2093 1639 a(\(if) p Fh 2212 1639 a(j) p Fn(x) p Fh(j) p Fp 2339 1639 a(=) p 2435 1639 a(1\),) p Fn 1757 1752 a(V) p Fj 1810 1766 a(!) p Fp 1861 1752 a(\(0\)) p Fn(;) p Fp 2093 1752 a(\(if) p Fn 2212 1752 a(x) p Fp 2289 1752 a(=) p 2385 1752 a(0\),) 1757 1865 y(0) p Fn(;) p Fp 2093 1865 a(\(otherwise\).) 448 2056 y @beginspecial @setspecial @endspecial(By) p 591 2056 a(\(2.4\),) p 833 2056 a(the) p 990 2056 a(pro) s(duct) p 1331 2056 a(is) p 1423 2056 a(giv) m(en) p 1660 2056 a(b) m(y) p Fn 1080 2271 a(hc) p Fp 1197 2271 a(=) p Fn 1293 2271 a(\031) p Fp 1348 2271 a(\() p Fn(H) p Fj 1459 2285 a(!) p Fn 1509 2271 a(C) p Fp 1581 2271 a(\)) p 1642 2271 a(=) p Fi 1766 2191 a(X) p Fj 1737 2389 a(z) p Fm 1773 2389 a(2) p Fg(Z) p 1836 2389 a(Z) p Ff 1879 2364 a(d) p Fn 1930 2271 a(h) p Fp(\() p Fn(T) p Fm 2083 2234 a(\000) p Fj(z) p Fn 2179 2271 a(!) s(;) p 2279 2271 a(x) p Fh 2351 2271 a(\000) p Fn 2442 2271 a(z) p Fp 2488 2271 a(\)) p Fn(c) p Fp(\() p Fn(!) s(;) p 2697 2271 a(z) p Fp 2743 2271 a(\)) p Fn(:) 448 2570 y @beginspecial @setspecial @endspecial Fp(First) p 666 2570 a(of) p 765 2570 a(all,) p 913 2570 a(w) m(e) p 1043 2570 a(compute) p 1407 2570 a(\() p Fn(h) p Fh(r) p Fj 1570 2584 a(n) p Fn 1617 2570 a(c) p Fp(\)\() p Fn(!) s(;) p 1826 2570 a(x) p Fp(\)) p Fh 1925 2570 a(\000) p Fp 2008 2570 a(\() p Fh(r) p Fj 2119 2584 a(n) p Fp 2167 2570 a(\() p Fn(hc) p Fp(\)\)\() p Fn(!) s(;) p 2498 2570 a(x) p Fp(\).) p 2652 2570 a(By) p 2790 2570 a(de\014nition) p 3190 2570 a(of) p Fh 3289 2570 a(r) p Fj 3365 2584 a(n) p Fp 3412 2570 a(,) 448 2694 y(w) m(e) p 582 2694 a(ha) m(v) m(e) 798 2910 y(\() p Fn(h) p Fh(r) p Fj 961 2924 a(n) p Fn 1008 2910 a(c) p Fp(\)\() p Fn(!) s(;) p 1217 2910 a(x) p Fp(\)) p 1331 2910 a(=) p Fi 1568 2829 a(X) p Fj 1427 3028 a(z) p Fm 1463 3028 a(2) p Fg(Z) p 1526 3028 a(Z) p Ff 1569 3002 a(d) p Fj 1605 3028 a(;) p Fm(j) p Fj(z) p Fc 1678 3037 a(1) p Fm 1711 3028 a(j\024) p Fj(n) p Fn 1844 2910 a(h) p Fp(\() p Fn(T) p Fm 1997 2872 a(\000) p Fj(z) p Fn 2092 2910 a(!) s(;) p 2192 2910 a(x) p Fh 2264 2910 a(\000) p Fn 2355 2910 a(z) p Fp 2401 2910 a(\)) p Fn 2451 2910 a(z) p Fl 2493 2924 a(1) p Fn 2549 2910 a(c) p Fp(\() p Fn(!) s(;) p 2723 2910 a(z) p Fp 2769 2910 a(\)) p 448 2910 a(\(3.2\)) 1331 3175 y(+) p Fi 1568 3094 a(X) p Fj 1427 3293 a(z) p Fm 1463 3293 a(2) p Fg(Z) p 1526 3293 a(Z) p Ff 1569 3267 a(d) p Fj 1605 3293 a(;) p Fm(j) p Fj(z) p Fc 1678 3302 a(1) p Fm 1711 3293 a(j) p Fj(>n) p Fn 1844 3175 a(h) p Fp(\() p Fn(T) p Fm 1997 3137 a(\000) p Fj(z) p Fn 2092 3175 a(!) s(;) p 2192 3175 a(x) p Fh 2264 3175 a(\000) p Fn 2355 3175 a(z) p Fp 2401 3175 a(\)\(sgn) p Fn 2604 3175 a(z) p Fl 2646 3189 a(1) p Fp 2686 3175 a(\)) p Fn 2736 3175 a(n) p 2806 3175 a(c) p Fp(\() p Fn(!) s(;) p 2980 3175 a(z) p Fp 3026 3175 a(\)) p Fn(;) p Fp 491 3767 a(\() p Fh(r) p Fj 602 3781 a(n) p Fp 649 3767 a(\() p Fn(hc) p Fp(\)\)\() p Fn(!) s(;) p 980 3767 a(x) p Fp(\)) p 1095 3767 a(=) p Fi 1191 3520 a(8) 1191 3594 y(>) 1191 3619 y(>) 1191 3644 y(>) 1191 3669 y(<) 1191 3819 y(>) 1191 3843 y(>) 1191 3868 y(>) 1191 3893 y(:) p Fn 1280 3598 a(x) p Fl 1332 3612 a(1) p Fi 1430 3517 a(X) p Fj 1401 3715 a(z) p Fm 1437 3715 a(2) p Fg(Z) p 1500 3715 a(Z) p Ff 1543 3690 a(d) p Fn 1594 3598 a(h) p Fp(\() p Fn(T) p Fm 1747 3560 a(\000) p Fj(z) p Fn 1842 3598 a(!) s(;) p 1942 3598 a(x) p Fh 2015 3598 a(\000) p Fn 2106 3598 a(z) p Fp 2152 3598 a(\)) p Fn(c) p Fp(\() p Fn(!) s(;) p 2361 3598 a(z) p Fp 2407 3598 a(\)) p Fn(;) p Fp 2832 3598 a(\(if) p Fh 2951 3598 a(j) p Fn(x) p Fl 3028 3612 a(1) p Fh 3068 3598 a(j) p 3118 3598 a(\024) p Fn 3214 3598 a(n) p Fp(\),) 1280 3849 y(\(sgn) p Fn 1477 3849 a(x) p Fl 1529 3863 a(1) p Fp 1568 3849 a(\)) p Fn(n) p Fi 1702 3768 a(X) p Fj 1674 3967 a(z) p Fm 1710 3967 a(2) p Fg(Z) p 1773 3967 a(Z) p Ff 1815 3941 a(d) p Fn 1866 3849 a(h) p Fp(\() p Fn(T) p Fm 2019 3811 a(\000) p Fj(z) p Fn 2115 3849 a(!) s(;) p 2215 3849 a(x) p Fh 2287 3849 a(\000) p Fn 2378 3849 a(z) p Fp 2424 3849 a(\)) p Fn(c) p Fp(\() p Fn(!) s(;) p 2633 3849 a(z) p Fp 2679 3849 a(\)) p Fn(;) p Fp 2832 3849 a(\(if) p Fh 2951 3849 a(j) p Fn(x) p Fl 3028 3863 a(1) p Fh 3068 3849 a(j) p Fn 3118 3849 a(>) p 3214 3849 a(n) p Fp(\).) 448 4081 y(\(3.3\)) p Fn 448 4296 a(h) p Fp(\() p Fn(T) p Fm 601 4263 a(\000) p Fj(z) p Fn 696 4296 a(!) s(;) p 796 4296 a(x) p Fh 867 4296 a(\000) p Fn 957 4296 a(z) p Fp 1003 4296 a(\)) p Fh 1063 4296 a(6) p Fp(=) p 1159 4296 a(0) p 1234 4296 a(only) p 1433 4296 a(if) p Fh 1516 4296 a(j) p Fn(x) p Fh 1611 4296 a(\000) p Fn 1701 4296 a(z) p Fh 1747 4296 a(j) p 1797 4296 a(\024) p Fp 1893 4296 a(1,) p 1994 4296 a(and) p 2170 4296 a(th) m(us) p 2369 4296 a(the) p 2525 4296 a(sums) p 2752 4296 a(in) p 2857 4296 a(\(3.2\),) p 3099 4296 a(\(3.3\)) p 3316 4296 a(are) 448 4421 y(\014nite) p 684 4421 a(sums) p 916 4421 a(and) p 1096 4421 a(they) p 1304 4421 a(mak) m(e) p 1545 4421 a(sense) p 1781 4421 a(for) p 1924 4421 a(eac) m(h) p 2132 4421 a(\() p Fn(!) s(;) p 2267 4421 a(x) p Fp(\)) p Fh 2386 4421 a(2) p Fp 2477 4421 a(\012) p Fh 2565 4421 a(\002) p Fk 2658 4421 a(Z) p 2678 4421 a(Z) p Fj 2733 4384 a(d) p Fp 2774 4421 a(.) p 2850 4421 a(W) p 2935 4421 a(e) p 3009 4421 a(divide) p 3283 4421 a(in) m(to) 448 4546 y(sev) m(eral) p 747 4546 a(cases.) 589 4670 y @beginspecial @setspecial @endspecial Fo(Case) p 812 4670 a(A) p Fp 910 4670 a(\() p Fh(j) p Fn(x) p Fl 1022 4684 a(1) p Fh 1062 4670 a(j) p 1113 4670 a(\024) p Fn 1209 4670 a(n) p Fp(\)) 1897 5225 y(24) p eop %%Page: 25 25 25 24 bop 589 573 a @beginspecial @setspecial @endspecial Fp(In) p 703 573 a(this) p 880 573 a(case,) p 1098 573 a(w) m(e) p 1232 573 a(ha) m(v) m(e) 961 756 y(\() p Fn(h) p Fh(r) p Fj 1124 770 a(n) p Fn 1171 756 a(c) p Fp(\)\() p Fn(!) s(;) p 1380 756 a(x) p Fp(\)) p Fh 1489 756 a(\000) p Fp 1580 756 a(\() p Fh(r) p Fj 1691 770 a(n) p Fp 1738 756 a(\() p Fn(hc) p Fp(\)\)\() p Fn(!) s(;) p 2069 756 a(x) p Fp(\)) p 448 756 a(\(3.4\)) 1052 905 y(=) p Fi 1190 824 a(X) p Fm 1148 1013 a(j) p Fj(z) p Fc 1201 1022 a(1) p Fm 1235 1013 a(j\024) p Fj(n) p Fp 1352 905 a(\() p Fn(z) p Fl 1429 919 a(1) p Fh 1489 905 a(\000) p Fn 1580 905 a(x) p Fl 1632 919 a(1) p Fp 1671 905 a(\)) p Fn(h) p Fp(\() p Fn(T) p Fm 1859 868 a(\000) p Fj(z) p Fn 1955 905 a(!) s(;) p 2055 905 a(x) p Fh 2127 905 a(\000) p Fn 2218 905 a(z) p Fp 2264 905 a(\)) p Fn(c) p Fp(\() p Fn(!) s(;) p 2473 905 a(z) p Fp 2519 905 a(\)) 1143 1160 y(+) p Fi 1271 1079 a(X) p Fm 1228 1267 a(j) p Fj(z) p Fc 1281 1276 a(1) p Fm 1315 1267 a(j) p Fj(>n) p Fp 1433 1160 a(\(\(sgn) p Fn 1666 1160 a(z) p Fl 1708 1174 a(1) p Fp 1747 1160 a(\)) p Fn(n) p Fh 1857 1160 a(\000) p Fn 1948 1160 a(x) p Fl 2000 1174 a(1) p Fp 2040 1160 a(\)) p Fn(h) p Fp(\() p Fn(T) p Fm 2228 1122 a(\000) p Fj(z) p Fn 2323 1160 a(!) s(;) p 2423 1160 a(x) p Fh 2496 1160 a(\000) p Fn 2587 1160 a(z) p Fp 2633 1160 a(\)) p Fn(c) p Fp(\() p Fn(!) s(;) p 2842 1160 a(z) p Fp 2888 1160 a(\)) 448 1422 y @beginspecial @setspecial @endspecial(The) p 635 1422 a(second) p 928 1422 a(term) p 1144 1422 a(of) p 1248 1422 a(RHS) p 1463 1422 a(is) p 1554 1422 a(nonzero) p 1892 1422 a(only) p 2091 1422 a(if) p Fn 2174 1422 a(x) p Fl 2226 1436 a(1) p Fp 2290 1422 a(=) p Fn 2386 1422 a(n) p Fp(,) p Fn 2496 1422 a(z) p Fl 2538 1436 a(1) p Fp 2603 1422 a(=) p Fn 2699 1422 a(n) p Fp 2773 1422 a(+) p 2863 1422 a(1,) p 2963 1422 a(or) p Fn 3074 1422 a(x) p Fl 3126 1436 a(1) p Fp 3191 1422 a(=) p Fh 3287 1422 a(\000) p Fn(n) p Fp(,) p Fn 448 1546 a(z) p Fl 490 1560 a(1) p Fp 555 1546 a(=) p Fh 651 1546 a(\000) p Fp(\() p Fn(n) p Fp 829 1546 a(+) p 916 1546 a(1\).) p 1062 1546 a(In) p 1174 1546 a(either) p 1431 1546 a(case,) p 1647 1546 a(\(sgn) p Fn 1844 1546 a(z) p Fl 1886 1560 a(1) p Fp 1926 1546 a(\)) p Fn(n) p Fh 2033 1546 a(\000) p Fn 2121 1546 a(x) p Fl 2173 1560 a(1) p Fp 2237 1546 a(=) p 2333 1546 a(0.) p 2444 1546 a(Therefore,) p 2880 1546 a(if) p Fh 2962 1546 a(j) p Fn(x) p Fl 3039 1560 a(1) p Fh 3078 1546 a(j) p 3129 1546 a(\024) p Fn 3225 1546 a(n) p Fp(,) p 3334 1546 a(w) m(e) 448 1671 y(ha) m(v) m(e) p Fh 1036 1854 a(j) p Fp(\() p Fn(h) p Fh(r) p Fj 1224 1868 a(n) p Fn 1272 1854 a(c) p Fp(\)\() p Fn(!) s(;) p 1481 1854 a(x) p Fp(\)) p Fh 1595 1854 a(\000) p Fp 1691 1854 a(\() p Fh(r) p Fj 1802 1868 a(n) p Fp 1849 1854 a(\() p Fn(hc) p Fp(\)\)\() p Fn(!) s(;) p 2180 1854 a(x) p Fp(\)) p Fh(j) p Fp 448 1854 a(\(3.5\)) p Fh 1595 2003 a(\024) p 1691 2003 a(j) p Fn(c) p Fp(\() p Fn(!) s(;) p 1890 2003 a(x) p Fp 1963 2003 a(+) p Fe 2054 2003 a(e) p Fl 2102 2017 a(1) p Fp 2141 2003 a(\)) p Fh(j) p Fp 2222 2003 a(+) p Fh 2313 2003 a(j) p Fn(c) p Fp(\() p Fn(!) s(;) p 2512 2003 a(x) p Fh 2585 2003 a(\000) p Fe 2676 2003 a(e) p Fl 2724 2017 a(1) p Fp 2764 2003 a(\)) p Fh(j) p Fn(;) 448 2186 y @beginspecial @setspecial @endspecial Fp(where) p Fe 711 2186 a(e) p Fl 759 2200 a(1) p Fp 824 2186 a(:=) p 945 2186 a(\(1) p Fn(;) p Fp 1065 2186 a(0) p Fn(;) p Fh 1150 2186 a(\001) p 1190 2186 a(\001) p 1230 2186 a(\001) p Fn 1273 2186 a(;) p Fp 1313 2186 a(0\)) p Fh 1420 2186 a(2) p Fk 1506 2186 a(Z) p 1526 2186 a(Z) p Fj 1580 2149 a(d) p Fp 1621 2186 a(.) 589 2311 y @beginspecial @setspecial @endspecial Fo(Case) p 812 2311 a(B) p Fp 907 2311 a(\() p Fh(j) p Fn(x) p Fl 1019 2325 a(1) p Fh 1059 2311 a(j) p Fn 1109 2311 a(>) p 1205 2311 a(n) p Fp(\)) 589 2435 y @beginspecial @setspecial @endspecial(In) p 703 2435 a(this) p 880 2435 a(case,) p 1098 2435 a(w) m(e) p 1232 2435 a(ha) m(v) m(e) 537 2618 y(\() p Fn(h) p Fh(r) p Fj 700 2632 a(n) p Fn 747 2618 a(c) p Fp(\)\() p Fn(!) s(;) p 956 2618 a(x) p Fp(\)) p Fh 1070 2618 a(\000) p Fp 1166 2618 a(\() p Fh(r) p Fj 1277 2632 a(n) p Fp 1324 2618 a(\() p Fn(hc) p Fp(\)\)\() p Fn(!) s(;) p 1655 2618 a(x) p Fp(\)) 1070 2767 y(=) p Fi 1307 2687 a(X) p Fj 1166 2885 a(z) p Fm 1202 2885 a(2) p Fg(Z) p 1265 2885 a(Z) p Ff 1308 2860 a(d) p Fj 1344 2885 a(;) p Fm(j) p Fj(z) p Fc 1417 2894 a(1) p Fm 1451 2885 a(j\024) p Fj(n) p Fp 1568 2767 a(\() p Fn(z) p Fl 1645 2781 a(1) p Fh 1705 2767 a(\000) p Fp 1796 2767 a(\(sgn) p Fn 1994 2767 a(x) p Fl 2046 2781 a(1) p Fp 2085 2767 a(\)) p Fn(n) p Fp(\)) p Fn(h) p Fp(\() p Fn(T) p Fm 2363 2730 a(\000) p Fj(z) p Fn 2459 2767 a(!) s(;) p 2559 2767 a(x) p Fh 2631 2767 a(\000) p Fn 2722 2767 a(z) p Fp 2768 2767 a(\)) p Fn(c) p Fp(\() p Fn(!) s(;) p 2977 2767 a(z) p Fp 3023 2767 a(\)) 1070 3032 y(+) p Fi 1307 2952 a(X) p Fj 1166 3150 a(z) p Fm 1202 3150 a(2) p Fg(Z) p 1265 3150 a(Z) p Ff 1308 3125 a(d) p Fj 1344 3150 a(;) p Fm(j) p Fj(z) p Fc 1417 3159 a(1) p Fm 1451 3150 a(j) p Fj(>n) p Fp 1568 3032 a(\(\(sgn) p Fn 1801 3032 a(z) p Fl 1843 3046 a(1) p Fp 1883 3032 a(\)) p Fh 1938 3032 a(\000) p Fp 2029 3032 a(\(sgn) p Fn 2227 3032 a(x) p Fl 2279 3046 a(1) p Fp 2318 3032 a(\)\)) p Fn 2403 3032 a(n) p 2473 3032 a(h) p Fp(\() p Fn(T) p Fm 2626 2995 a(\000) p Fj(z) p Fn 2722 3032 a(!) s(;) p 2822 3032 a(x) p Fh 2894 3032 a(\000) p Fn 2985 3032 a(z) p Fp 3031 3032 a(\)) p Fn(c) p Fp(\() p Fn(!) s(;) p 3240 3032 a(z) p Fp 3286 3032 a(\)) p Fn(:) 448 3305 y @beginspecial @setspecial @endspecial Fp(The) p 635 3305 a(\014rst) p 823 3305 a(term) p 1040 3305 a(of) p 1143 3305 a(RHS) p 1359 3305 a(in) p 1465 3305 a(the) p 1621 3305 a(ab) s(o) m(v) m(e) p 1879 3305 a(expression) p 2317 3305 a(v) p 2360 3305 a(anishes) p 2674 3305 a(b) m(y) p 2800 3305 a(the) p 2956 3305 a(same) p 3184 3305 a(reason) 448 3429 y(as) p 567 3429 a(in) p 679 3429 a(Case) p 904 3429 a(A.) p 1034 3429 a(The) p 1228 3429 a(second) p 1528 3429 a(term) p 1752 3429 a(is) p 1850 3429 a(nonzero) p 2196 3429 a(only) p 2402 3429 a(if) p Fh 2492 3429 a(j) p Fn(x) p Fl 2569 3443 a(1) p Fh 2609 3429 a(j) p Fn 2670 3429 a(>) p 2778 3429 a(n) p Fp(,) p Fh 2896 3429 a(j) p Fn(z) p Fl 2963 3443 a(1) p Fh 3003 3429 a(j) p Fn 3065 3429 a(>) p 3172 3429 a(n) p Fp(,) p 3291 3429 a(and) p Fh 448 3554 a(j) p Fn(x) p Fh 552 3554 a(\000) p Fn 648 3554 a(z) p Fh 694 3554 a(j) p 760 3554 a(\024) p Fp 871 3554 a(1,) p 983 3554 a(in) p 1097 3554 a(whic) m(h) p 1366 3554 a(case) p 1568 3554 a(sgn) p Fn 1739 3554 a(x) p Fl 1791 3568 a(1) p Fp 1870 3554 a(=) p 1980 3554 a(sgn) p Fn 2151 3554 a(z) p Fl 2193 3568 a(1) p Fp 2232 3554 a(.) p 2325 3554 a(Th) m(us,) p 2591 3554 a(the) p 2757 3554 a(second) p 3059 3554 a(term) p 3285 3554 a(also) 448 3678 y(v) p 491 3678 a(anishes.) 589 3803 y @beginspecial @setspecial @endspecial(Next,) p 839 3803 a(w) m(e) p 975 3803 a(compute) p 1346 3803 a(\(\() p Fh(r) p Fj 1492 3817 a(n) p Fn 1539 3803 a(c) p Fp(\)) p Fn(h) p Fp(\)\() p Fn(!) s(;) p 1835 3803 a(x) p Fp(\)) p Fh 1946 3803 a(\000) p Fp 2039 3803 a(\() p Fh(r) p Fj 2150 3817 a(n) p Fp 2197 3803 a(\() p Fn(ch) p Fp(\)\)\() p Fn(!) s(;) p 2528 3803 a(x) p Fp(\).) p 2689 3803 a(Eac) m(h) p 2917 3803 a(term) p 3137 3803 a(is) p 3230 3803 a(giv) m(en) 448 3928 y(b) m(y) 506 4110 y(\(\() p Fh(r) p Fj 652 4124 a(n) p Fn 699 4110 a(c) p Fp(\)) p Fn(h) p Fp(\)\() p Fn(!) s(;) p 995 4110 a(x) p Fp(\)) p 1110 4110 a(=) p Fi 1411 4030 a(X) p Fj 1206 4228 a(z) p Fm 1242 4228 a(2) p Fg(Z) p 1305 4228 a(Z) p Ff 1347 4203 a(d) p Fj 1384 4228 a(;) p Fm(j) p Fj(x) p Fc 1464 4237 a(1) p Fm 1497 4228 a(\000) p Fj(z) p Fc 1585 4237 a(1) p Fm 1619 4228 a(j\024) p Fj(n) p Fp 1737 4110 a(\() p Fn(x) p Fl 1824 4124 a(1) p Fh 1884 4110 a(\000) p Fn 1975 4110 a(z) p Fl 2017 4124 a(1) p Fp 2056 4110 a(\)) p Fn 2106 4110 a(c) p Fp(\() p Fn(T) p Fm 2246 4073 a(\000) p Fj(z) p Fn 2342 4110 a(!) s(;) p 2442 4110 a(x) p Fh 2514 4110 a(\000) p Fn 2605 4110 a(z) p Fp 2651 4110 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 2873 4110 a(z) p Fp 2919 4110 a(\)) 1110 4375 y(+) p Fi 1411 4295 a(X) p Fj 1206 4493 a(z) p Fm 1242 4493 a(2) p Fg(Z) p 1305 4493 a(Z) p Ff 1347 4468 a(d) p Fj 1384 4493 a(;) p Fm(j) p Fj(x) p Fc 1464 4502 a(1) p Fm 1497 4493 a(\000) p Fj(z) p Fc 1585 4502 a(1) p Fm 1619 4493 a(j) p Fj(>n) p Fn 1752 4375 a(n) p Fp 1822 4375 a(sgn) p 1984 4375 a(\() p Fn(x) p Fl 2071 4389 a(1) p Fh 2131 4375 a(\000) p Fn 2222 4375 a(z) p Fl 2264 4389 a(1) p Fp 2303 4375 a(\)) p Fn(c) p Fp(\() p Fn(T) p Fm 2478 4338 a(\000) p Fj(z) p Fn 2574 4375 a(!) s(;) p 2674 4375 a(x) p Fh 2746 4375 a(\000) p Fn 2837 4375 a(z) p Fp 2883 4375 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 3105 4375 a(z) p Fp 3151 4375 a(\)) p Fn(;) p Fp 506 4809 a(\() p Fh(r) p Fj 617 4823 a(n) p Fp 664 4809 a(\() p Fn(ch) p Fp(\)\)\() p Fn(!) s(;) p 995 4809 a(x) p Fp(\)) p 1110 4809 a(=) p Fi 1206 4562 a(8) 1206 4637 y(>) 1206 4662 y(>) 1206 4687 y(>) 1206 4712 y(<) 1206 4861 y(>) 1206 4886 y(>) 1206 4911 y(>) 1206 4936 y(:) 1324 4560 y(X) p Fj 1295 4758 a(z) p Fm 1331 4758 a(2) p Fg(Z) p 1394 4758 a(Z) p Ff 1436 4732 a(d) p Fn 1488 4640 a(x) p Fl 1540 4654 a(1) p Fn 1579 4640 a(c) p Fp(\() p Fn(T) p Fm 1719 4603 a(\000) p Fj(z) p Fn 1814 4640 a(!) s(;) p 1914 4640 a(x) p Fh 1987 4640 a(\000) p Fn 2078 4640 a(z) p Fp 2124 4640 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 2346 4640 a(z) p Fp 2392 4640 a(\)) p Fn(;) p Fp 2832 4640 a(\(if) p Fh 2951 4640 a(j) p Fn(x) p Fl 3028 4654 a(1) p Fh 3068 4640 a(j) p 3118 4640 a(\024) p Fn 3214 4640 a(n) p Fp(\),) p Fi 1324 4811 a(X) p Fj 1295 5010 a(z) p Fm 1331 5010 a(2) p Fg(Z) p 1394 5010 a(Z) p Ff 1436 4984 a(d) p Fn 1488 4892 a(n) p Fp(\(sgn) p Fn 1740 4892 a(x) p Fl 1792 4906 a(1) p Fp 1831 4892 a(\)) p Fn(c) p Fp(\() p Fn(T) p Fm 2006 4854 a(\000) p Fj(z) p Fn 2102 4892 a(!) s(;) p 2202 4892 a(x) p Fh 2274 4892 a(\000) p Fn 2365 4892 a(z) p Fp 2411 4892 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 2633 4892 a(z) p Fp 2679 4892 a(\)) p Fn(;) p Fp 2832 4892 a(\(if) p Fh 2951 4892 a(j) p Fn(x) p Fl 3028 4906 a(1) p Fh 3068 4892 a(j) p Fn 3118 4892 a(>) p 3214 4892 a(n) p Fp(\).) 1897 5225 y(25) p eop %%Page: 26 26 26 25 bop 589 573 a @beginspecial @setspecial @endspecial Fo(Case) p 812 573 a(C) p Fp 908 573 a(\() p Fh(j) p Fn(x) p Fl 1020 587 a(1) p Fh 1060 573 a(j) p 1110 573 a(\024) p Fn 1206 573 a(n) p Fp(\)) 589 697 y @beginspecial @setspecial @endspecial(In) p 703 697 a(this) p 880 697 a(case,) p 1098 697 a(w) m(e) p 1232 697 a(ha) m(v) m(e) 460 887 y(\(\() p Fh(r) p Fj 606 901 a(n) p Fn 653 887 a(c) p Fp(\)) p Fn(h) p Fp(\)\() p Fn(!) s(;) p 949 887 a(x) p Fp(\)) p Fh 1064 887 a(\000) p Fp 1160 887 a(\() p Fh(r) p Fj 1271 901 a(n) p Fp 1318 887 a(\() p Fn(ch) p Fp(\)\)\() p Fn(!) s(;) p 1649 887 a(x) p Fp(\)) 1064 1036 y(=) p Fi 1365 955 a(X) p Fj 1160 1154 a(z) p Fm 1196 1154 a(2) p Fg(Z) p 1259 1154 a(Z) p Ff 1301 1128 a(d) p Fj 1338 1154 a(;) p Fm(j) p Fj(x) p Fc 1418 1163 a(1) p Fm 1451 1154 a(\000) p Fj(z) p Fc 1539 1163 a(1) p Fm 1573 1154 a(j\024) p Fj(n) p Fp 1691 1036 a(\() p Fh(\000) p Fn(z) p Fl 1839 1050 a(1) p Fp 1879 1036 a(\)) p Fn(c) p Fp(\() p Fn(T) p Fm 2054 999 a(\000) p Fj(z) p Fn 2149 1036 a(!) s(;) p 2249 1036 a(x) p Fh 2321 1036 a(\000) p Fn 2412 1036 a(z) p Fp 2458 1036 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 2680 1036 a(z) p Fp 2726 1036 a(\)) 1064 1301 y(+) p Fi 1365 1220 a(X) p Fj 1160 1419 a(z) p Fm 1196 1419 a(2) p Fg(Z) p 1259 1419 a(Z) p Ff 1301 1393 a(d) p Fj 1338 1419 a(;) p Fm(j) p Fj(x) p Fc 1418 1428 a(1) p Fm 1451 1419 a(\000) p Fj(z) p Fc 1539 1428 a(1) p Fm 1573 1419 a(j) p Fj(>n) p Fp 1691 1301 a(\() p Fn(n) p Fp 1796 1301 a(sgn) p 1958 1301 a(\() p Fn(x) p Fl 2045 1315 a(1) p Fh 2105 1301 a(\000) p Fn 2196 1301 a(z) p Fl 2238 1315 a(1) p Fp 2277 1301 a(\)) p Fh 2333 1301 a(\000) p Fn 2424 1301 a(x) p Fl 2476 1315 a(1) p Fp 2515 1301 a(\)) p Fn(c) p Fp(\() p Fn(T) p Fm 2690 1264 a(\000) p Fj(z) p Fn 2786 1301 a(!) s(;) p 2886 1301 a(x) p Fh 2958 1301 a(\000) p Fn 3049 1301 a(z) p Fp 3095 1301 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 3317 1301 a(z) p Fp 3363 1301 a(\)) p Fn(:) 448 1580 y @beginspecial @setspecial @endspecial Fp(The) p 633 1580 a(second) p 925 1580 a(term) p 1140 1580 a(is) p 1230 1580 a(nonzero) p 1566 1580 a(only) p 1764 1580 a(if) p Fn 1845 1580 a(x) p Fl 1897 1594 a(1) p Fp 1962 1580 a(=) p Fh 2058 1580 a(\000) p Fn(n) p Fp(,) p Fn 2237 1580 a(z) p Fl 2279 1594 a(1) p Fp 2344 1580 a(=) p 2440 1580 a(1,) p 2539 1580 a(or) p Fn 2649 1580 a(x) p Fl 2701 1594 a(1) p Fp 2765 1580 a(=) p Fn 2861 1580 a(n) p Fp(,) p Fn 2970 1580 a(z) p Fl 3012 1594 a(1) p Fp 3077 1580 a(=) p Fh 3173 1580 a(\000) p Fp(1.) p 3354 1580 a(In) 448 1705 y(either) p 706 1705 a(case,) p 924 1705 a(the) p 1080 1705 a(second) p 1374 1705 a(term) p 1591 1705 a(v) p 1634 1705 a(anishes.) p 1984 1705 a(Hence,) p 2279 1705 a(if) p Fh 2362 1705 a(j) p Fn(x) p Fl 2439 1719 a(1) p Fh 2479 1705 a(j) p 2530 1705 a(\024) p Fn 2626 1705 a(n) p Fp(,) p 2736 1705 a(w) m(e) p 2870 1705 a(ha) m(v) m(e) p Fi 802 1797 a(\014) 802 1847 y(\014) 802 1896 y(\014) p Fp 830 1894 a(\(\() p Fh(r) p Fj 976 1908 a(n) p Fn 1023 1894 a(c) p Fp(\)) p Fn(h) p Fp(\)\() p Fn(!) s(;) p 1319 1894 a(x) p Fp(\)) p Fh 1429 1894 a(\000) p Fp 1520 1894 a(\() p Fh(r) p Fj 1631 1908 a(n) p Fp 1678 1894 a(\() p Fn(ch) p Fp(\)\)\() p Fn(!) s(;) p 2009 1894 a(x) p Fp(\)) p Fi 2096 1797 a(\014) 2096 1847 y(\014) 2096 1896 y(\014) p Fh 2151 1894 a(\024) p Fi 2270 1813 a(X) p Fm 2247 2002 a(j) p Fj(z) p Fm 2303 2002 a(j) p Fl(=1) p Fh 2427 1894 a(j) p Fn(c) p Fp(\() p Fn(T) p Fm 2592 1857 a(\000) p Fj(z) p Fn 2688 1894 a(!) s(;) p 2788 1894 a(x) p Fh 2860 1894 a(\000) p Fn 2951 1894 a(z) p Fp 2997 1894 a(\)) p Fh(j) p Fn(:) p Fp 448 1894 a(\(3.6\)) 589 2168 y @beginspecial @setspecial @endspecial Fo(Case) p 812 2168 a(D) p Fp 911 2168 a(\() p Fh(j) p Fn(x) p Fl 1023 2182 a(1) p Fh 1063 2168 a(j) p Fn 1114 2168 a(>) p 1210 2168 a(n) p Fp(\)) 589 2292 y @beginspecial @setspecial @endspecial(In) p 703 2292 a(this) p 880 2292 a(case,) p 1098 2292 a(w) m(e) p 1232 2292 a(ha) m(v) m(e) 580 2482 y(\(\() p Fh(r) p Fj 726 2496 a(n) p Fn 773 2482 a(c) p Fp(\)) p Fn 848 2482 a(h) p Fp(\)\() p Fn(!) s(;) p 1070 2482 a(x) p Fp(\)) p Fh 1178 2482 a(\000) p Fp 1269 2482 a(\() p Fh(r) p Fj 1380 2496 a(n) p Fp 1427 2482 a(\() p Fn(ch) p Fp(\)\)\() p Fn(!) s(;) p 1758 2482 a(x) p Fp(\)) 696 2631 y(=) p Fi 1053 2550 a(X) p Fj 848 2749 a(z) p Fm 884 2749 a(2) p Fg(Z) p 947 2749 a(Z) p Ff 989 2723 a(d) p Fj 1025 2749 a(;) p Fm(j) p Fj(x) p Fc 1105 2758 a(1) p Fm 1139 2749 a(\000) p Fj(z) p Fc 1227 2758 a(1) p Fm 1261 2749 a(j\024) p Fj(n) p Fp 1379 2631 a(\(\() p Fn(x) p Fl 1501 2645 a(1) p Fh 1561 2631 a(\000) p Fn 1652 2631 a(z) p Fl 1694 2645 a(1) p Fp 1734 2631 a(\)) p Fh 1789 2631 a(\000) p Fp 1880 2631 a(\(sgn) p Fn 2077 2631 a(x) p Fl 2129 2645 a(1) p Fp 2169 2631 a(\)) p Fn 2219 2631 a(n) p Fp(\)) p Fn 2324 2631 a(c) p Fp(\() p Fn(T) p Fm 2464 2594 a(\000) p Fj(z) p Fn 2560 2631 a(!) s(;) p 2660 2631 a(x) p Fh 2732 2631 a(\000) p Fn 2823 2631 a(z) p Fp 2869 2631 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 3091 2631 a(z) p Fp 3137 2631 a(\)) 696 2896 y(+) p Fi 1053 2815 a(X) p Fj 848 3014 a(z) p Fm 884 3014 a(2) p Fg(Z) p 947 3014 a(Z) p Ff 989 2988 a(d) p Fj 1025 3014 a(;) p Fm(j) p Fj(x) p Fc 1105 3023 a(1) p Fm 1139 3014 a(\000) p Fj(z) p Fc 1227 3023 a(1) p Fm 1261 3014 a(j) p Fj(>n) p Fn 1394 2896 a(n) p Fp 1464 2896 a(\(sgn) p 1661 2896 a(\() p Fn(x) p Fl 1748 2910 a(1) p Fh 1808 2896 a(\000) p Fn 1899 2896 a(z) p Fl 1941 2910 a(1) p Fp 1981 2896 a(\)) p Fh 2036 2896 a(\000) p Fp 2127 2896 a(sgn) p Fn 2289 2896 a(x) p Fl 2341 2910 a(1) p Fp 2380 2896 a(\)) p Fn 2430 2896 a(c) p Fp(\() p Fn(T) p Fm 2570 2859 a(\000) p Fj(z) p Fn 2666 2896 a(!) s(;) p 2766 2896 a(x) p Fh 2839 2896 a(\000) p Fn 2929 2896 a(z) p Fp 2975 2896 a(\)) p Fn(h) p Fp(\() p Fn(!) s(;) p 3197 2896 a(z) p Fp 3243 2896 a(\)) p Fn(:) 448 3175 y @beginspecial @setspecial @endspecial Fp(By) p 606 3175 a(the) p 778 3175 a(similar) p 1091 3175 a(argumen) m(t) p 1513 3175 a(as) p 1640 3175 a(in) p 1761 3175 a(Case) p 1993 3175 a(B,) p 2128 3175 a(C,) p 2265 3175 a(w) m(e) p 2413 3175 a(see) p 2575 3175 a(that) p 2787 3175 a(the) p 2959 3175 a(RHS) p 3190 3175 a(in) p 3311 3175 a(the) 448 3300 y(ab) s(o) m(v) m(e) p 708 3300 a(expression) p 1148 3300 a(v) p 1191 3300 a(anishes.) p 1545 3300 a(By) p 1690 3300 a(\(3.5\),) p 1935 3300 a(\(3.6\),) p 2179 3300 a(w) m(e) p 2315 3300 a(conclude) p 2690 3300 a(that) p 2889 3300 a([) p Fh(L) p Fj 2977 3314 a(H) p Ff 3035 3322 a(!) p Fn 3084 3300 a(;) p Fh 3124 3300 a(r) p Fj 3200 3314 a(n) p Fp 3247 3300 a(]) p Fn(C) p Fp 3376 3300 a(is) 448 3424 y(uniformly) p 863 3424 a(b) s(ounded) p 1234 3424 a(in) p Fh 1340 3424 a(L) p Fl 1403 3391 a(2) p Fp 1472 3424 a(w.r.t.) p Fn 1725 3424 a(n) p Fp(.) 589 3549 y @beginspecial @setspecial @endspecial(\(2\)) p 726 3549 a(Let) p Fn 880 3549 a(C) p Fp 977 3549 a(:=) p 1098 3549 a(\() p Fn(z) p Fh 1180 3549 a(\000) q(L) p Fj 1315 3563 a(H) p Ff 1373 3571 a(!) p Fp 1422 3549 a(\)) p Fm 1457 3516 a(\000) p Fl(1) p Fn 1552 3549 a(A) p Fp(,) p 1668 3549 a(for) p Fn 1798 3549 a(A) p Fh 1891 3549 a(2) p 1977 3549 a(D) p Fp 2050 3549 a(\() p Fn(@) p Fl 2133 3563 a(1) p Fp 2173 3549 a(\),) p 2256 3549 a(Im) p Fn 2386 3549 a(z) p Fh 2457 3549 a(6) p Fp(=) p 2553 3549 a(0.) p 2661 3549 a(Then,) p Fn 2916 3549 a(C) p Fh 3013 3549 a(2) p 3099 3549 a(D) p Fp 3172 3549 a(\() p Fh(L) p Fj 3270 3563 a(H) p Ff 3328 3571 a(!) p Fp 3377 3549 a(\),) 448 3673 y(and) p 625 3673 a(as) p 737 3673 a(discussed) p 1132 3673 a(in) p 1238 3673 a(the) p 1395 3673 a(pro) s(of) p 1632 3673 a(of) p 1736 3673 a(Prop) s(osition) p 2225 3673 a(2.8,) p Fh 2397 3673 a(r) p Fj 2473 3687 a(n) p Fn 2520 3673 a(C) p Fh 2617 3673 a(2) p 2702 3673 a(D) p Fp 2775 3673 a(\() p Fh(L) p Fj 2873 3687 a(H) p Ff 2931 3695 a(!) p Fp 2980 3673 a(\).) p 3081 3673 a(Then,) p Fh 660 3863 a(r) p Fj 736 3877 a(n) p Fp 783 3863 a(\() p Fn(z) p Fh 885 3863 a(\000) p 976 3863 a(L) p Fj 1039 3877 a(H) p Ff 1097 3885 a(!) p Fp 1145 3863 a(\)) p Fm 1180 3825 a(\000) p Fl(1) p Fn 1275 3863 a(A) p Fp 1368 3863 a(=) p Fh 1464 3863 a(r) p Fj 1540 3877 a(n) p Fn 1587 3863 a(C) p Fp 1368 4012 a(=) p 1464 4012 a(\() p Fn(z) p Fh 1566 4012 a(\000) p 1657 4012 a(L) p Fj 1720 4026 a(H) p Ff 1778 4034 a(!) p Fp 1827 4012 a(\)) p Fm 1862 3975 a(\000) p Fl(1) p Fp 1956 4012 a(\() p Fn(z) p Fh 2058 4012 a(\000) p 2149 4012 a(L) p Fj 2212 4026 a(H) p Ff 2270 4034 a(!) p Fp 2319 4012 a(\)) p Fh(r) p Fj 2430 4026 a(n) p Fn 2477 4012 a(C) p Fp 1368 4162 a(=) p 1464 4162 a(\() p Fn(z) p Fh 1566 4162 a(\000) p 1657 4162 a(L) p Fj 1720 4176 a(H) p Ff 1778 4184 a(!) p Fp 1827 4162 a(\)) p Fm 1862 4124 a(\000) p Fl(1) p Fh 1956 4162 a(r) p Fj 2032 4176 a(n) p Fp 2079 4162 a(\(\() p Fn(z) p Fh 2216 4162 a(\000) p 2307 4162 a(L) p Fj 2370 4176 a(H) p Ff 2428 4184 a(!) p Fp 2477 4162 a(\)) p Fn(C) p Fp 2584 4162 a(\)) 1646 4311 y(+\() p Fn(z) p Fh 1819 4311 a(\000) p 1910 4311 a(L) p Fj 1973 4325 a(H) p Ff 2031 4333 a(!) p Fp 2079 4311 a(\)) p Fm 2114 4274 a(\000) p Fl(1) p Fp 2209 4311 a([\() p Fn(z) p Fh 2336 4311 a(\000) p 2427 4311 a(L) p Fj 2490 4325 a(H) p Ff 2548 4333 a(!) p Fp 2596 4311 a(\)) p Fn(;) p Fh 2671 4311 a(r) p Fj 2747 4325 a(n) p Fp 2795 4311 a(]) p Fn(C) p Fp 1368 4460 a(=) p 1464 4460 a(\() p Fn(z) p Fh 1566 4460 a(\000) p 1657 4460 a(L) p Fj 1720 4474 a(H) p Ff 1778 4482 a(!) p Fp 1827 4460 a(\)) p Fm 1862 4423 a(\000) p Fl(1) p Fh 1956 4460 a(r) p Fj 2032 4474 a(n) p Fn 2079 4460 a(A) p Fh 2167 4460 a(\000) p Fp 2258 4460 a(\() p Fn(z) p Fh 2360 4460 a(\000) p 2451 4460 a(L) p Fj 2514 4474 a(H) p Ff 2572 4482 a(!) p Fp 2621 4460 a(\)) p Fm 2656 4423 a(\000) p Fl(1) p Fp 2750 4460 a([) p Fh(L) p Fj 2838 4474 a(H) p Ff 2896 4482 a(!) p Fn 2945 4460 a(;) p Fh 2985 4460 a(r) p Fj 3061 4474 a(n) p Fp 3108 4460 a(]) p Fn(C) q(:) 448 4650 y @beginspecial @setspecial @endspecial Fp(By) p 585 4650 a(\(1\)) p 725 4650 a(of) p 823 4650 a(Lemma) p 1141 4650 a(3.1,) p 1308 4650 a(the) p 1459 4650 a(RHS) p 1668 4650 a(in) p 1768 4650 a(the) p 1919 4650 a(ab) s(o) m(v) m(e) p 2170 4650 a(expression) p 2603 4650 a(is) p 2688 4650 a(uniformly) p 3096 4650 a(b) s(ounded) 448 4774 y(in) p Fh 554 4774 a(L) p Fl 617 4741 a(2) p Fp 687 4774 a(w.r.t.) p Fn 940 4774 a(n) p Fp(.) p 1060 4774 a(On) p 1211 4774 a(the) p 1368 4774 a(other) p 1606 4774 a(hand,) p 1858 4774 a(b) m(y) p 1984 4774 a(monotone) p 2404 4774 a(con) m(v) m (ergence) p 2906 4774 a(theorem,) p Fh 1309 4964 a(k) p Fn(@) p Fl 1402 4978 a(1) p Fn 1442 4964 a(C) p Fh 1514 4964 a(k) p Fl 1559 4926 a(2) p Fm 1559 4991 a(L) p Fc 1608 4972 a(2) p Fp 1672 4964 a(=) p 1796 4964 a(lim) p Fj 1768 5014 a(n) p Fm(!1) p Fh 1967 4964 a(kr) p Fj 2088 4978 a(n) p Fn 2135 4964 a(C) p Fh 2207 4964 a(k) p Fl 2252 4926 a(2) p Fm 2252 4991 a(L) p Fc 2301 4972 a(2) p Fn 2364 4964 a(<) p Fh 2460 4964 a(1) p Fn(:) p Fp 1897 5225 a(26) p eop %%Page: 27 27 27 26 bop 448 573 a @beginspecial @setspecial @endspecial Fp(Therefore,) p 890 573 a(w) m(e) p 1027 573 a(ha) m(v) m(e) p Fh 1240 573 a(k) p Fn(@) p Fl 1333 587 a(1) p Fp 1373 573 a(\() p Fn(z) p Fh 1478 573 a(\000) p 1571 573 a(L) p Fj 1634 587 a(H) p Ff 1692 595 a(!) p Fp 1740 573 a(\)) p Fm 1775 540 a(\000) p Fl(1) p Fn 1870 573 a(A) p Fh(k) p Fm 1983 593 a(L) p Fc 2032 574 a(2) p Fn 2102 573 a(<) p Fh 2204 573 a(1) p Fp(,) p 2354 573 a(and) p Fn 2535 573 a(@) p Fl 2583 587 a(1) p Fp 2622 573 a(\() p Fn(z) p Fh 2726 573 a(\000) p 2820 573 a(L) p Fj 2883 587 a(H) p Ff 2941 595 a(!) p Fp 2989 573 a(\)) p Fm 3024 540 a(\000) p Fl(1) p Fn 3119 573 a(A) p Fh 3218 573 a(2) p 3310 573 a(L) p Fl 3373 540 a(2) p Fp 3412 573 a(.) 448 697 y(Lemma) p 773 697 a(3.1) p 919 697 a(is) p 1011 697 a(pro) m(v) m(ed.) p 1342 633 60 4 v 1342 722 4 89 v 1398 722 V 1342 725 60 4 v Fe 448 884 a(Remark) p 846 884 a(3.1) p 1025 884 a @beginspecial @setspecial @endspecial Fo(\(3.4\)) p 1252 884 a(shows) p Fn 1351 1084 a(h) p Fp(\() p Fh(r) p Fj 1514 1098 a(n) p Fn 1561 1084 a(c) p Fp(\)) p Fh 1656 1084 a(\000) p 1747 1084 a(r) p Fj 1823 1098 a(n) p Fp 1870 1084 a(\() p Fn(hc) p Fp(\)) p Fh 2057 1084 a(!) p 2174 1084 a(\000) p Fp(\() p Fn(@) p Fl 2328 1098 a(1) p Fn 2367 1084 a(h) p Fp(\)) p Fn 2469 1084 a(c;) 448 1285 y @beginspecial @setspecial @endspecial Fo(in) p Fp 581 1262 a(~) p Fh 560 1285 a(L) p Fl 623 1252 a(2) p Fo 694 1285 a(as) p Fn 811 1285 a(n) p Fh 890 1285 a(!) p 1007 1285 a(1) p Fo(,) p 1158 1285 a(which) p 1414 1285 a(we) p 1548 1285 a(ne) p 1636 1285 a(e) p 1673 1285 a(de) p 1756 1285 a(d) p 1836 1285 a(in) p 1948 1285 a(the) p 2099 1285 a(pr) p 2178 1285 a(o) p 2219 1285 a(of) p 2328 1285 a(of) p 2435 1285 a(Pr) p 2530 1285 a(op) p 2617 1285 a(osition) p 2918 1285 a(2.8.) 448 1471 y @beginspecial @setspecial @endspecial(Pr) p 543 1471 a(o) p 584 1471 a(of) p 692 1471 a(of) p 799 1471 a(Pr) p 894 1471 a(op) p 981 1471 a(osition) p 1283 1471 a(3.1) 589 1596 y @beginspecial @setspecial @endspecial Fp(Let) p Fn 752 1596 a(A) p Fh 846 1596 a(2) p 932 1596 a(D) p Fp 1005 1596 a(\() p Fn(@) p Fl 1088 1610 a(1) p Fp 1127 1596 a(\),) p 1218 1596 a(Im) p Fn 1357 1596 a(z) p Fh 1429 1596 a(6) p Fp(=) p 1525 1596 a(0.) p 1636 1596 a(Then,) 880 1796 y(\() p Fn(z) p Fh 987 1796 a(\000) p 1083 1796 a(L) p Fj 1146 1810 a(H) p Ff 1204 1821 a(!) r(;) p Fd(E) p Fp 1309 1796 a(\)) p Fm 1344 1758 a(\000) p Fl(1) p Fn 1438 1796 a(A) p Fh 1527 1796 a(\000) p Fp 1618 1796 a(\() p Fn(z) p Fh 1720 1796 a(\000) p 1810 1796 a(L) p Fj 1873 1810 a(H) p Ff 1931 1818 a(!) p Fp 1980 1796 a(\)) p Fm 2015 1758 a(\000) p Fl(1) p Fn 2110 1796 a(A) p Fp 987 1945 a(=) p 1083 1945 a(\() p Fn(z) p Fh 1185 1945 a(\000) p 1275 1945 a(L) p Fj 1338 1959 a(H) p Ff 1396 1970 a(!) r(;) p Fd(E) p Fp 1501 1945 a(\)) p Fm 1536 1908 a(\000) p Fl(1) p Fp 1631 1945 a(\() p Fn(z) p Fh 1733 1945 a(\000) p 1824 1945 a(L) p Fj 1887 1959 a(H) p Ff 1945 1967 a(!) p Fp 1993 1945 a(\)\() p Fn(z) p Fh 2131 1945 a(\000) p 2222 1945 a(L) p Fj 2285 1959 a(H) p Ff 2343 1967 a(!) p Fp 2391 1945 a(\)) p Fm 2426 1908 a(\000) p Fl(1) p Fn 2521 1945 a(A) p Fh 1174 2095 a(\000) p Fp(\() p Fn(z) p Fh 1346 2095 a(\000) p 1437 2095 a(L) p Fj 1500 2109 a(H) p Ff 1558 2120 a(!) r(;) p Fd(E) p Fp 1663 2095 a(\)) p Fm 1698 2057 a(\000) p Fl(1) p Fp 1793 2095 a(\() p Fn(z) p Fh 1895 2095 a(\000) p 1985 2095 a(L) p Fj 2048 2109 a(H) p Ff 2106 2117 a(!) p Fh 2175 2095 a(\000) p 2266 2095 a(E) p Fn 2322 2095 a(@) p Fl 2370 2109 a(1) p Fp 2410 2095 a(\)\() p Fn(z) p Fh 2547 2095 a(\000) p 2638 2095 a(L) p Fj 2701 2109 a(H) p Ff 2759 2117 a(!) p Fp 2808 2095 a(\)) p Fm 2843 2057 a(\000) p Fl(1) p Fn 2937 2095 a(A) p Fp 987 2244 a(=) p 1083 2244 a(\() p Fn(z) p Fh 1185 2244 a(\000) p 1275 2244 a(L) p Fj 1338 2258 a(H) p Ff 1396 2269 a(!) r(;) p Fd(E) p Fp 1501 2244 a(\)) p Fm 1536 2207 a(\000) p Fl(1) p Fh 1631 2244 a(E) p Fn 1687 2244 a(@) p Fl 1735 2258 a(1) p Fp 1775 2244 a(\() p Fn(z) p Fh 1877 2244 a(\000) p 1968 2244 a(L) p Fj 2031 2258 a(H) p Ff 2089 2266 a(!) p Fp 2137 2244 a(\)) p Fm 2172 2207 a(\000) p Fl(1) p Fn 2267 2244 a(A:) 448 2445 y @beginspecial @setspecial @endspecial Fp(In) p 562 2445 a(the) p 719 2445 a(second) p 1012 2445 a(step,) p 1230 2445 a(w) m(e) p 1363 2445 a(used) p 1571 2445 a(Lemma) p 1896 2445 a(3.1.) p 2077 2381 V 2077 2470 4 89 v 2133 2470 V 2077 2473 60 4 v 589 2660 a @beginspecial @setspecial @endspecial(F) p 640 2660 a(rom) p 843 2660 a(no) m(w) p 1047 2660 a(on,) p 1217 2660 a(w) m(e) p 1365 2660 a(will) p 1551 2660 a(carry) p 1801 2660 a(out) p 1977 2660 a(eac) m(h) p 2196 2660 a(op) s(erations) p 2654 2660 a(in) p 2774 2660 a(the) p 2945 2660 a(de\014nition) p 3364 2660 a(of) p Fn 448 2785 a(\033) p Fl 500 2799 a(2) p Fp 540 2785 a(\() p Fn(!) s(;) p 675 2785 a(\017) p Fj 712 2799 a(F) p Fp 771 2785 a(\).) p Fe 448 2971 a(Lemma) p 819 2971 a(3.2) p 998 2971 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1094 2971 a(P) p Fj 1152 2985 a(\017) p Ff 1181 2996 a(F) p Fo 1268 2971 a(satis\014es) p 1609 2971 a(Assumption) p 2109 2971 a(\(1.6\),) 589 3096 y @beginspecial @setspecial @endspecial Fp 854 3296 a(lim) p Fm 861 3356 a(E) p 904 3356 a(#) p Fl(0) p Fp 1011 3234 a(1) p 1006 3275 57 4 v Fh 1006 3358 a(E) p Fi 1087 3181 a(Z) p Fm 1170 3207 a(1) p Fl 1133 3370 a(0) p Fn 1260 3296 a(dt) p 1365 3296 a(\016) t(e) p Fm 1451 3258 a(\000) p Fj(t\016) p Fh 1570 3296 a(T) p Fp 1642 3296 a(\() p Fn(e) p Fj 1719 3258 a(itH) p Ff 1826 3269 a(!) r(;) p Fd(E) p Fn 1933 3296 a(i) p Fp([) p Fn(H) p Fj 2065 3310 a(!) p Fn 2115 3296 a(;) p 2155 3296 a(x) p Fl 2207 3310 a(1) p Fp 2247 3296 a(]) p Fn(e) p Fm 2314 3258 a(\000) p Fj(itH) p Ff 2476 3269 a(!) r(;) p Fd(E) p Fn 2582 3296 a(P) p Fj 2640 3310 a(\017) p Ff 2669 3321 a(F) p Fp 2724 3296 a(\)) 1454 3491 y(=) p Fn 1570 3491 a(i) p 1626 3491 a(<) p Fp 1722 3491 a(\() p Fh(\000) p Fn(i\016) p Fh 1924 3491 a(\000) p 2014 3491 a(L) p Fj 2077 3505 a(H) p Ff 2135 3513 a(!) p Fp 2184 3491 a(\)) p Fm 2219 3453 a(\000) p Fl(1) p Fn 2314 3491 a(@) p Fl 2362 3505 a(1) p Fn 2401 3491 a(H) p Fj 2477 3505 a(!) p Fn 2527 3491 a(;) p 2567 3491 a(@) p Fl 2615 3505 a(1) p Fn 2656 3491 a(P) p Fj 2714 3505 a(\017) p Ff 2743 3516 a(F) p Fn 2823 3491 a(>) p Fm 2894 3510 a(L) p Fc 2943 3491 a(2) p Fn 3006 3491 a(:) 448 3940 y @beginspecial @setspecial @endspecial Fo(Pr) p 543 3940 a(o) p 584 3940 a(of.) p Fp 727 3940 a(By) p 868 3940 a(Prop) s(osition) p 1355 3940 a(2.7,) p Fn 1525 3940 a(e) p Fj 1567 3907 a(itH) p Ff 1674 3918 a(!) r(;) p Fd(E) p Fn 1780 3940 a(i) p Fp([) p Fn(H) p Fj 1912 3954 a(!) p Fn 1963 3940 a(;) p 2003 3940 a(x) p Fl 2055 3954 a(1) p Fp 2094 3940 a(]) p Fn(e) p Fm 2161 3907 a(\000) p Fj(itH) p Ff 2323 3918 a(!) r(;) p Fd(E) p Fp 2455 3940 a(=) p Fh 2551 3940 a(\000) p Fn(e) p Fj 2664 3893 a(it) p Fm(L) p Ff 2762 3904 a(H) 2812 3921 y(!) r(;) p Fd(E) p Fp 2921 3940 a(\() p Fn(i@) p Fl 3035 3954 a(1) p Fn 3076 3940 a(H) p Fj 3152 3954 a(!) p Fp 3202 3940 a(\),) p 3291 3940 a(and) 448 4065 y(b) m(y) p 574 4065 a(Prop) s(osition) p 1063 4065 a(2.5) p 1210 4065 a(and) p 1386 4065 a(the) p 1542 4065 a(fact) p 1721 4065 a(that) p 1918 4065 a(iden) m(tit) m(y) p 2254 4065 a(op) s(erator) p 2620 4065 a(on) p Fn 2746 4065 a(l) p Fl 2775 4032 a(2) p Fp 2814 4065 a(\() p Fk(Z) p 2869 4065 a(Z) p Fj 2924 4028 a(d) p Fp 2965 4065 a(\)) p 3030 4065 a(b) s(elongs) p 3356 4065 a(to) p Fh 448 4189 a(L) p Fl 511 4156 a(2) p Fp 550 4189 a(,) p Fn 606 4189 a(P) p Fj 664 4203 a(\017) p Ff 693 4214 a(F) p Fh 773 4189 a(2) p 859 4189 a(L) p Fl 922 4156 a(2) p Fp 961 4189 a(.) p 1027 4189 a(Then,) p Fi 853 4301 a(Z) p Fm 936 4327 a(1) p Fl 900 4489 a(0) p Fn 1026 4416 a(dt) p 1132 4416 a(\016) t(e) p Fm 1218 4378 a(\000) p Fj(t\016) p Fh 1336 4416 a(T) p Fp 1409 4416 a(\() p Fn(e) p Fj 1486 4378 a(itH) p Ff 1593 4389 a(!) r(;) p Fd(E) p Fn 1699 4416 a(i) p Fp([) p Fn(H) p Fj 1831 4430 a(!) p Fn 1882 4416 a(;) p 1922 4416 a(x) p Fl 1974 4430 a(1) p Fp 2014 4416 a(]) p Fn(e) p Fm 2081 4378 a(\000) p Fj(itH) p Ff 2243 4389 a(!) r(;) p Fd(E) p Fn 2349 4416 a(P) p Fj 2407 4430 a(\017) p Ff 2436 4441 a(F) p Fp 2491 4416 a(\)) 1220 4640 y(=) p Fh 1336 4640 a(\000) p Fi 1422 4525 a(Z) p Fm 1505 4551 a(1) p Fl 1468 4713 a(0) p Fn 1595 4640 a(dt) p 1700 4640 a(\016) s(e) p Fm 1785 4602 a(\000) p Fj(t\016) p Fn 1930 4640 a(<) p 2026 4640 a(e) p Fj 2068 4592 a(it) p Fm(L) p Ff 2166 4603 a(H) 2216 4620 y(!) r(;) p Fd(E) p Fp 2326 4640 a(\() p Fn(i@) p Fl 2440 4654 a(1) p Fn 2480 4640 a(H) p Fj 2556 4654 a(!) p Fp 2606 4640 a(\)) p Fn(;) p 2681 4640 a(P) p Fj 2739 4654 a(\017) p Ff 2768 4665 a(F) p Fn 2849 4640 a(>) p Fm 2920 4659 a(L) p Fc 2969 4640 a(2) p Fp 1220 4827 a(=) p 1336 4827 a(\() p Fh(\000) p Fn(\016) p Fp 1485 4827 a(\)) p Fn 1547 4827 a(<) p Fp 1643 4827 a(\() p Fh(\000) p Fn(i\016) p Fh 1844 4827 a(\000) p 1935 4827 a(L) p Fj 1998 4841 a(H) p Ff 2056 4852 a(!) r(;) p Fd(E) p Fp 2161 4827 a(\)) p Fm 2196 4789 a(\000) p Fl(1) p Fn 2291 4827 a(@) p Fl 2339 4841 a(1) p Fn 2378 4827 a(H) p Fj 2454 4841 a(!) p Fn 2504 4827 a(;) p 2544 4827 a(P) p Fj 2602 4841 a(\017) p Ff 2631 4852 a(F) p Fn 2712 4827 a(>) p Fm 2783 4847 a(L) p Fc 2832 4828 a(2) p Fp 1220 4976 a(=) p 1336 4976 a(\() p Fh(\000) p Fn(\016) p Fp 1485 4976 a(\)) p Fn 1547 4976 a(<) p 1643 4976 a(@) p Fl 1691 4990 a(1) p Fn 1730 4976 a(H) p Fj 1806 4990 a(!) p Fn 1856 4976 a(;) p Fp 1896 4976 a(\() p Fn(i\016) p Fh 2027 4976 a(\000) p 2118 4976 a(L) p Fj 2181 4990 a(H) p Ff 2239 5001 a(!) r(;) p Fd(E) p Fp 2344 4976 a(\)) p Fm 2379 4939 a(\000) p Fl(1) p Fn 2474 4976 a(P) p Fj 2532 4990 a(\017) p Ff 2561 5001 a(F) p Fn 2641 4976 a(>) p Fm 2712 4996 a(L) p Fc 2761 4977 a(2) p Fn 2824 4976 a(:) p Fp 1897 5225 a(27) p eop %%Page: 28 28 28 27 bop 448 573 a @beginspecial @setspecial @endspecial Fp(By) p 591 573 a(Assumption) p 1095 573 a(\(1.6\),) p Fn 1337 573 a(P) p Fj 1395 587 a(\017) p Ff 1424 598 a(F) p Fh 1504 573 a(2) p 1590 573 a(D) p Fp 1663 573 a(\() p Fn(@) p Fl 1746 587 a(1) p Fp 1786 573 a(\).) p 1887 573 a(Then,) p 2149 573 a(b) m(y) p 2276 573 a(Prop) s(osition) p 2765 573 a(3.1,) 750 789 y(=) p 859 789 a(\() p Fh(\000) p Fn(\016) p Fp 1008 789 a(\)) p Fn 1069 789 a(<) p 1165 789 a(@) p Fl 1213 803 a(1) p Fn 1253 789 a(H) p Fj 1329 803 a(!) p Fn 1379 789 a(;) p Fp 1419 789 a(\() p Fn(i\016) p Fh 1550 789 a(\000) p 1641 789 a(L) p Fj 1704 803 a(H) p Ff 1762 811 a(!) p Fp 1810 789 a(\)) p Fm 1845 751 a(\000) p Fl(1) p Fn 1940 789 a(P) p Fj 1998 803 a(\017) p Ff 2027 814 a(F) p Fn 2107 789 a(>) p Fm 2178 808 a(L) p Fc 2227 789 a(2) p Fp 950 938 a(+\() p Fh(\000) p Fn(\016) p Fp 1170 938 a(\)) p Fh(E) p Fn 1287 938 a(<) p 1383 938 a(@) p Fl 1431 952 a(1) p Fn 1471 938 a(H) p Fj 1547 952 a(!) p Fn 1597 938 a(;) p Fp 1637 938 a(\() p Fn(i\016) p Fh 1768 938 a(\000) p 1859 938 a(L) p Fj 1922 952 a(H) p Ff 1980 963 a(!) r(;) p Fd(E) p Fp 2085 938 a(\)) p Fm 2120 901 a(\000) p Fl(1) p Fn 2214 938 a(@) p Fl 2262 952 a(1) p Fp 2302 938 a(\() p Fn(i\016) p Fh 2433 938 a(\000) p 2524 938 a(L) p Fj 2587 952 a(H) p Ff 2645 960 a(!) p Fp 2693 938 a(\)) p Fm 2728 901 a(\000) p Fl(1) p Fn 2823 938 a(P) p Fj 2881 952 a(\017) p Ff 2910 963 a(F) p Fn 2990 938 a(>) p Fm 3061 958 a(L) p Fc 3110 939 a(2) p Fp 737 1088 a(=:) p Fn 859 1088 a(I) p Fp 926 1088 a(+) p Fn 1017 1088 a(I) p 1064 1088 a(I) p 1111 1088 a(:) 448 1303 y @beginspecial @setspecial @endspecial Fp(F) p 499 1303 a(or) p 611 1303 a(b) s(ounded) p 983 1303 a(Borel) p 1224 1303 a(measurable) p 1699 1303 a(function) p Fn 2055 1303 a(f) p Fp 2110 1303 a(\() p Fn(\025) p Fp(\)) p 2264 1303 a(on) p 2390 1303 a(I) p 2408 1303 a(R) o(,) p 2530 1303 a(b) m(y) p 2656 1303 a(de\014nition,) p 3085 1303 a(it) p 3176 1303 a(is) p 3267 1303 a(easy) 448 1428 y(to) p 553 1428 a(see) p 693 1428 a(that) p Fn 883 1428 a(H) p Fj 959 1442 a(!) p Fn 1009 1428 a(f) p Fp 1064 1428 a(\() p Fn(H) p Fj 1175 1442 a(!) p Fp 1225 1428 a(\)\() p Fn(!) p Fp 1371 1428 a(;) p Fn 1411 1428 a(x;) p 1503 1428 a(y) p Fp 1551 1428 a(\)) p 1612 1428 a(=) p Fn 1708 1428 a(f) p Fp 1763 1428 a(\() p Fn(H) p Fj 1874 1442 a(!) p Fp 1923 1428 a(\)) p Fn(H) p Fj 2034 1442 a(!) p Fp 2085 1428 a(\() p Fn(!) p Fp 2195 1428 a(;) p Fn 2235 1428 a(x;) p 2327 1428 a(y) p Fp 2375 1428 a(\),) p 2461 1428 a(and) p 2631 1428 a(th) m(us) p Fh 2825 1428 a(L) p Fj 2888 1442 a(H) p Ff 2946 1450 a(!) p Fn 2994 1428 a(f) p Fp 3049 1428 a(\() p Fn(H) p Fj 3160 1442 a(!) p Fp 3210 1428 a(\)) p 3270 1428 a(=) p 3366 1428 a(0.) 448 1553 y(Hence,) p Fn 1394 1677 a(P) p Fj 1452 1691 a(\017) p Ff 1481 1702 a(F) p Fp 1561 1677 a(=) p 1657 1677 a(\() p Fn(i\016) p Fp 1766 1677 a(\)) p Fm 1801 1640 a(\000) p Fl(1) p Fp 1897 1677 a(\() p Fn(i\016) p Fh 2028 1677 a(\000) p 2119 1677 a(L) p Fj 2182 1691 a(H) p Ff 2240 1699 a(!) p Fp 2289 1677 a(\)) p Fn(P) p Fj 2382 1691 a(\017) p Ff 2411 1702 a(F) p Fn 2466 1677 a(:) p Fp 448 1677 a(\(3.7\)) 448 1856 y @beginspecial @setspecial @endspecial(By) p 591 1856 a(Prop) s(osition) p 1080 1856 a(2.8) p 1227 1856 a(and) p 1404 1856 a(\(3.7\),) p Fn 1095 2071 a(I) p Fp 1167 2071 a(=) p Fn 1263 2071 a(i) p 1320 2071 a(<) p 1416 2071 a(@) p Fl 1464 2085 a(1) p Fn 1504 2071 a(H) p Fj 1580 2085 a(!) p Fn 1630 2071 a(;) p 1670 2071 a(P) p Fj 1728 2085 a(\017) p Ff 1757 2096 a(F) p Fn 1837 2071 a(>) p Fm 1908 2091 a(L) p Fc 1957 2072 a(2) p Fp 1167 2221 a(=) p 1263 2221 a(0) p Fn(;) 1048 2370 y(I) p 1095 2370 a(I) p Fp 1167 2370 a(=) p Fn 1263 2370 a(i) p Fh(E) p Fn 1376 2370 a(<) p 1472 2370 a(@) p Fl 1520 2384 a(1) p Fn 1560 2370 a(H) p Fj 1636 2384 a(!) p Fn 1686 2370 a(;) p Fp 1726 2370 a(\() p Fn(i\016) p Fh 1857 2370 a(\000) p 1948 2370 a(L) p Fj 2011 2384 a(H) p Ff 2069 2395 a(!) r(;) p Fd(E) p Fp 2174 2370 a(\)) p Fm 2209 2333 a(\000) p Fl(1) p Fn 2303 2370 a(@) p Fl 2351 2384 a(1) p Fn 2391 2370 a(P) p Fj 2449 2384 a(\017) p Ff 2478 2395 a(F) p Fn 2558 2370 a(>) p Fm 2629 2390 a(L) p Fc 2678 2371 a(2) p Fp 1167 2520 a(=) p Fn 1263 2520 a(i) p Fh(E) p Fn 1376 2520 a(<) p Fp 1472 2520 a(\() p Fh(\000) p Fn(i\016) p Fh 1673 2520 a(\000) p 1764 2520 a(L) p Fj 1827 2534 a(H) p Ff 1885 2545 a(!) r(;) p Fd(E) p Fp 1990 2520 a(\)) p Fm 2025 2482 a(\000) p Fl(1) p Fn 2120 2520 a(@) p Fl 2168 2534 a(1) p Fn 2208 2520 a(H) p Fj 2284 2534 a(!) p Fn 2334 2520 a(;) p 2374 2520 a(@) p Fl 2422 2534 a(1) p Fn 2462 2520 a(P) p Fj 2520 2534 a(\017) p Ff 2549 2545 a(F) p Fn 2629 2520 a(>) p Fm 2700 2539 a(L) p Fc 2749 2521 a(2) p Fn 2812 2520 a(:) 448 2736 y @beginspecial @setspecial @endspecial Fp(Therefore,) 957 2911 y(1) p 952 2952 57 4 v Fh 952 3035 a(E) p Fi 1033 2858 a(Z) p Fm 1116 2884 a(1) p Fl 1079 3047 a(0) p Fn 1221 2973 a(\016) t(e) p Fm 1307 2935 a(\000) p Fj(t\016) p Fh 1426 2973 a(T) p Fp 1498 2973 a(\() p Fn(e) p Fj 1575 2935 a(itH) p Ff 1682 2946 a(!) r(;) p Fd(E) p Fn 1789 2973 a(i) p Fp([) p Fn(H) p Fj 1921 2987 a(!) p Fn 1971 2973 a(;) p 2011 2973 a(x) p Fl 2063 2987 a(1) p Fp 2103 2973 a(]) p Fn(e) p Fm 2170 2935 a(\000) p Fj(itH) p Ff 2332 2946 a(!) r(;) p Fd(E) p Fn 2438 2973 a(P) p Fj 2496 2987 a(\017) p Ff 2525 2998 a(F) p Fp 2580 2973 a(\)) p 448 2973 a(\(3.8\)) 1310 3160 y(=) p Fn 1426 3160 a(i) p 1482 3160 a(<) p Fp 1578 3160 a(\() p Fh(\000) p Fn(i\016) p Fh 1780 3160 a(\000) p 1870 3160 a(L) p Fj 1933 3174 a(H) p Ff 1991 3185 a(!) r(;) p Fd(E) p Fp 2096 3160 a(\)) p Fm 2131 3123 a(\000) p Fl(1) p Fn 2226 3160 a(@) p Fl 2274 3174 a(1) p Fn 2314 3160 a(H) p Fj 2390 3174 a(!) p Fn 2440 3160 a(;) p 2480 3160 a(@) p Fl 2528 3174 a(1) p Fn 2568 3160 a(P) p Fj 2626 3174 a(\017) p Ff 2655 3185 a(F) p Fn 2735 3160 a(>) p Fm 2806 3180 a(L) p Fc 2855 3161 a(2) p Fn 2918 3160 a(:) 448 3376 y @beginspecial @setspecial @endspecial Fp(Since) p Fn 686 3376 a(@) p Fl 734 3390 a(1) p Fn 773 3376 a(H) p Fj 849 3390 a(!) p Fh 925 3376 a(2) p 1010 3376 a(A) p Fl 1083 3390 a(0) p Fh 1148 3376 a(\032) p 1244 3376 a(D) p Fp 1317 3376 a(\() p Fn(@) p Fl 1400 3390 a(1) p Fp 1439 3376 a(\),) p 1530 3376 a(w) m(e) p 1664 3376 a(use) p 1821 3376 a(Prop) s(osition) p 2311 3376 a(3.1) p 2457 3376 a(again.) 781 3592 y(RHS) p 997 3592 a(of) p 1100 3592 a(\(3.8\)) 781 3741 y(=) p Fn 877 3741 a(i) p 933 3741 a(<) p Fp 1029 3741 a(\() p Fh(\000) p Fn(i\016) p Fh 1231 3741 a(\000) p 1321 3741 a(L) p Fj 1384 3755 a(H) p Ff 1442 3763 a(!) p Fp 1491 3741 a(\)) p Fm 1526 3704 a(\000) p Fl(1) p Fn 1621 3741 a(@) p Fl 1669 3755 a(1) p Fn 1708 3741 a(H) p Fj 1784 3755 a(!) p Fn 1834 3741 a(;) p 1874 3741 a(@) p Fl 1922 3755 a(1) p Fn 1963 3741 a(P) p Fj 2021 3755 a(\017) p Ff 2050 3766 a(F) p Fn 2130 3741 a(>) p Fm 2201 3761 a(L) p Fc 2250 3742 a(2) p Fp 781 3891 a(+) p Fn(i) p Fh(E) p Fn 964 3891 a(<) p Fp 1060 3891 a(\() p Fh(\000) p Fn(i\016) p Fh 1261 3891 a(\000) p 1352 3891 a(L) p Fj 1415 3905 a(H) p Ff 1473 3916 a(!) r(;) p Fd(E) p Fp 1578 3891 a(\)) p Fm 1613 3853 a(\000) p Fl(1) p Fn 1708 3891 a(@) p Fl 1756 3905 a(1) p Fp 1796 3891 a(\() p Fh(\000) p Fn(i\016) p Fh 1997 3891 a(\000) p 2088 3891 a(L) p Fj 2151 3905 a(H) p Ff 2209 3913 a(!) p Fp 2258 3891 a(\)) p Fm 2293 3853 a(\000) p Fl(1) p Fn 2387 3891 a(@) p Fl 2435 3905 a(1) p Fn 2475 3891 a(H) p Fj 2551 3905 a(!) p Fn 2601 3891 a(;) p 2641 3891 a(@) p Fl 2689 3905 a(1) p Fn 2729 3891 a(P) p Fj 2787 3905 a(\017) p Ff 2816 3916 a(F) p Fn 2896 3891 a(>) p Fm 2967 3910 a(L) p Fc 3016 3892 a(2) p Fn 3080 3891 a(:) 448 4107 y @beginspecial @setspecial @endspecial Fp(F) p 499 4107 a(or) p 620 4107 a(\014xed) p Fn 848 4107 a(\016) p 931 4107 a(>) p Fp 1041 4107 a(0,) p 1152 4107 a(the) p 1317 4107 a(second) p 1619 4107 a(term) p 1845 4107 a(go) s(es) p 2053 4107 a(to) p 2173 4107 a(zero) p 2373 4107 a(as) p Fh 2493 4107 a(E) p 2589 4107 a(#) p Fp 2673 4107 a(0.) p 2810 4107 a(Hence,) p 3116 4107 a(w) m(e) p 3258 4107 a(ha) m(v) m(e) 448 4231 y(Lemma) p 773 4231 a(3.2.) p 955 4167 60 4 v 955 4256 4 89 v 1010 4256 V 955 4259 60 4 v Fe 448 4480 a(Remark) p 846 4480 a(3.2) p 1025 4480 a @beginspecial @setspecial @endspecial Fo(The) p 1211 4480 a(e) p 1248 4480 a(quality) p Fn 1544 4480 a(I) p Fp 1617 4480 a(=) p 1714 4480 a(0) p Fo 1793 4480 a(c) p 1830 4480 a(orr) p 1947 4480 a(esp) p 2067 4480 a(onds) p 2283 4480 a(to) p 2393 4480 a(the) p 2545 4480 a(fact) p 2724 4480 a(that) p Fn 2911 4480 a(\033) p Fl 2963 4494 a(2) p Fp 3002 4480 a(\() p Fn(!) s(;) p 3137 4480 a(\017) p Fj 3174 4494 a(F) p Fp 3233 4480 a(\)) p 3295 4480 a(=) p 3392 4480 a(0) p Fo 448 4605 a(if) p Fh 537 4605 a(E) p Fp 618 4605 a(=) p 714 4605 a(0) p Fo(.) 448 4829 y @beginspecial @setspecial @endspecial Fp(The) p 632 4829 a(follo) m(wing) p 1012 4829 a(lemma) p 1302 4829 a(w) m(ould) p 1564 4829 a(b) s(e) p 1684 4829 a(useful) p 1941 4829 a(to) p 2049 4829 a(study) p 2296 4829 a(\014nite) p 2525 4829 a(temp) s(erature) p 3040 4829 a(prop) s(erties) 448 4953 y(of) p 551 4953 a(c) m(harge) p 836 4953 a(transp) s(ort,) p 1263 4953 a(though) p 1570 4953 a(w) m(e) p 1704 4953 a(will) p 1875 4953 a(not) p 2035 4953 a(use) p 2192 4953 a(it) p 2282 4953 a(in) p 2387 4953 a(the) p 2543 4953 a(pro) s(of) p 2780 4953 a(of) p 2883 4953 a(Theorem) p 3266 4953 a(1,) p 3366 4953 a(2.) 1897 5225 y(28) p eop %%Page: 29 29 29 28 bop Fe 448 573 a(Lemma) p 819 573 a(3.3) p 998 573 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1094 573 a(f) p Fj 1139 588 a(\014) s(;\017) p Ff 1231 599 a(F) p Fp 1284 573 a(\() p Fn(H) p Fj 1395 587 a(!) p Fp 1445 573 a(\)) p Fo 1513 573 a(satis\014es) p 1855 573 a(the) p 2006 573 a(fol) p 2108 573 a(lowing) p 2392 573 a(de) p 2475 573 a(c) p 2512 573 a(ay) p 2635 573 a(estimate) p Fe 1154 789 a(E) p Fh(j) p Fn(f) p Fj 1293 804 a(\014) s(;\017) p Ff 1385 815 a(F) p Fp 1438 789 a(\() p Fn(H) p Fj 1549 803 a(!) p Fp 1600 789 a(\)\() p Fn(!) p Fp 1745 789 a(;) p Fn 1785 789 a(x;) p 1877 789 a(y) p Fp 1925 789 a(\)) p Fh(j) p 2012 789 a(\024) p Fn 2108 789 a(C) p 2204 789 a(<) p 2300 789 a(x) p Fh 2373 789 a(\000) p Fn 2463 789 a(y) p 2537 789 a(>) p Fm 2608 751 a(\000) p Fj(\015) p Fn 2707 789 a(;) p Fp 448 789 a(\(3.9\)) 448 1005 y @beginspecial @setspecial @endspecial Fo(for) p 597 1005 a(some) p 832 1005 a(c) p 869 1005 a(onstant) p Fn 1198 1005 a(C) p 1300 1005 a(>) p Fp 1402 1005 a(0) p Fo 1483 1005 a(indep) p 1691 1005 a(endent) p 1990 1005 a(of) p Fn 2100 1005 a(x) p Fo(,) p Fn 2217 1005 a(y) p Fh 2295 1005 a(2) p Fk 2387 1005 a(Z) p 2406 1005 a(Z) p Fj 2461 968 a(d) p Fo 2501 1005 a(,) p Fn 2566 1005 a(\015) p 2649 1005 a(>) p 2750 1005 a(d) p Fp 2820 1005 a(+) p 2913 1005 a(2) p Fo(,) p 3023 1005 a(and) p Fn 3203 1005 a(\014) p 3290 1005 a(>) p Fp 3392 1005 a(0) p Fo 448 1129 a(\() p Fn(<) p 581 1129 a(x) p 659 1129 a(>) p Fp(:=) p 851 1129 a(1) p 916 1129 a(+) p Fh 1007 1129 a(j) p Fn(x) p Fh(j) p Fo(\),) p 1207 1129 a(then) p 1409 1129 a(we) p 1544 1129 a(have) p Fn 1667 1345 a(f) p Fj 1712 1360 a(\014) s(;\017) p Ff 1804 1371 a(F) p Fp 1858 1345 a(\() p Fn(H) p Fj 1969 1359 a(!) p Fp 2019 1345 a(\)) p Fh 2080 1345 a(!) p Fn 2196 1345 a(P) p Fj 2254 1359 a(\017) p Ff 2283 1370 a(F) p Fn 2338 1345 a(;) 1507 1494 y(@) p Fl 1555 1508 a(1) p Fn 1595 1494 a(f) p Fj 1640 1509 a(\014) s(;\017) p Ff 1732 1520 a(F) p Fp 1785 1494 a(\() p Fn(H) p Fj 1896 1508 a(!) p Fp 1947 1494 a(\)) p Fh 2007 1494 a(!) p Fn 2124 1494 a(@) p Fl 2172 1508 a(1) p Fn 2211 1494 a(P) p Fj 2269 1508 a(\017) p Ff 2298 1519 a(F) p Fn 2353 1494 a(;) 448 1710 y @beginspecial @setspecial @endspecial Fo(in) p Fh 560 1710 a(L) p Fl 623 1677 a(2) p Fo 662 1710 a(,) p 722 1710 a(as) p Fn 839 1710 a(\014) p Fh 920 1710 a(!) p 1036 1710 a(1) p Fo(.) 448 1959 y @beginspecial @setspecial @endspecial(Pr) p 543 1959 a(o) p 584 1959 a(of.) p Fp 728 1959 a(Since) p Fe 965 1959 a(P) p Fh(f) p Fn(\017) p Fj 1118 1973 a(F) p Fp 1208 1959 a(is) p 1300 1959 a(the) p 1456 1959 a(eigen) m(v) p 1698 1959 a(alue) p 1891 1959 a(of) p Fn 1994 1959 a(H) p Fj 2070 1973 a(!) p Fh 2120 1959 a(g) p Fp 2191 1959 a(=) p 2287 1959 a(0,) p Fn 1268 2175 a(f) p Fj 1313 2190 a(\014) s(;\017) p Ff 1405 2201 a(F) p Fp 1459 2175 a(\() p Fn(H) p Fj 1570 2189 a(!) p Fp 1620 2175 a(\)\() p Fn(!) p Fp 1766 2175 a(;) p Fn 1806 2175 a(x;) p 1898 2175 a(y) p Fp 1946 2175 a(\)) p Fh 2007 2175 a(!) p Fn 2124 2175 a(P) p Fj 2182 2189 a(\017) p Ff 2211 2200 a(F) p Fp 2265 2175 a(\() p Fn(!) p Fp 2376 2175 a(;) p Fn 2416 2175 a(x;) p 2508 2175 a(y) p Fp 2556 2175 a(\)) p Fn(;) 448 2391 y @beginspecial @setspecial @endspecial Fp(as) p Fn 560 2391 a(\014) p Fh 641 2391 a(!) p 758 2391 a(1) p Fp(,) p 904 2391 a(for) p 1043 2391 a(a.e.) p Fn 1220 2391 a(!) p Fp 1280 2391 a(.) p 1345 2391 a(Then,) p 1608 2391 a(b) m(y) p 1734 2391 a(dominated) p 2184 2391 a(con) m(v) m(ergence) p 2687 2391 a(theorem,) p Fi 1028 2508 a(Z) p Fl 1074 2697 a(\012) p Fn 1144 2623 a(d) p Fe(P) p Fi 1262 2526 a(\014) 1262 2576 y(\014) 1262 2625 y(\014) p Fn 1290 2623 a(f) p Fj 1335 2638 a(\014) s(;\017) p Ff 1427 2649 a(F) p Fp 1481 2623 a(\() p Fn(H) p Fj 1592 2637 a(!) p Fp 1642 2623 a(\)\() p Fn(!) p Fp 1788 2623 a(;) p Fn 1828 2623 a(x;) p Fp 1920 2623 a(0\)) p Fh 2022 2623 a(\000) p Fn 2113 2623 a(P) p Fj 2171 2637 a(\017) p Ff 2200 2648 a(F) p Fp 2255 2623 a(\() p Fn(!) p Fp 2365 2623 a(;) p Fn 2405 2623 a(x;) p Fp 2497 2623 a(0\)) p Fi 2577 2526 a(\014) 2577 2576 y(\014) 2577 2625 y(\014) p Fl 2606 2552 a(2) p Fh 2671 2623 a(!) p Fp 2787 2623 a(0) p Fn(;) 448 2880 y @beginspecial @setspecial @endspecial Fp(as) p Fn 569 2880 a(\014) p Fh 666 2880 a(!) p 797 2880 a(1) p Fp(,) p 955 2880 a(for) p 1103 2880 a(an) m(y) p Fn 1284 2880 a(x) p Fh 1376 2880 a(2) p Fk 1477 2880 a(Z) p 1497 2880 a(Z) p Fj 1552 2843 a(d) p Fp 1592 2880 a(.) p 1685 2880 a(Then,) p 1959 2880 a(b) m(y) p 2094 2880 a(\(3.9\)) p 2320 2880 a(and) p 2506 2880 a(dominated) p 2965 2880 a(con) m(v) m(ergence) 448 3004 y(theorem) p 802 3004 a(again,) p 1070 3004 a(w) m(e) p 1204 3004 a(can) p 1370 3004 a(easily) p 1621 3004 a(arriv) m(e) p 1879 3004 a(at) p 1990 3004 a(the) p 2147 3004 a(conclusion.) p 2622 2940 60 4 v 2622 3029 4 89 v 2678 3029 V 2622 3032 60 4 v 589 3253 a @beginspecial @setspecial @endspecial(T) p 647 3253 a(o) p 729 3253 a(study) p Fn 984 3253 a(\016) p Fh 1062 3253 a(#) p Fp 1142 3253 a(0) p 1223 3253 a(limit,) p 1472 3253 a(w) m(e) p 1611 3253 a(prepare) p 1945 3253 a(a) p 2026 3253 a(series) p 2275 3253 a(of) p 2384 3253 a(lemmas,) p 2744 3253 a(b) m(y) p 2876 3253 a(b) s(orro) m(wing) p 3311 3253 a(the) 448 3378 y(argumen) m(ts) p 891 3378 a(in) p 997 3378 a([2) q(].) p 1159 3378 a(F) p 1210 3378 a(or) p 1322 3378 a(the) p 1478 3378 a(sak) m(e) p 1676 3378 a(of) p 1779 3378 a(simplicit) m(y) p 2158 3378 a(,) p 2212 3378 a(w) m(e) p 2346 3378 a(write) p Fn 2578 3378 a(P) p Fp 2679 3378 a(instead) p 2993 3378 a(of) p Fn 3097 3378 a(P) p Fj 3155 3392 a(\017) p Ff 3184 3403 a(F) p Fp 3238 3378 a(.) p Fe 448 3577 a(Lemma) p 819 3577 a(3.4) p 998 3577 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1094 3577 a(P) p Fh 1190 3577 a(2) p 1276 3577 a(D) p Fp 1349 3577 a(\() p Fn(@) p Fl 1432 3591 a(1) p Fp 1471 3577 a(\)) p Fo(,) p 1567 3577 a(we) p 1702 3577 a(have) p Fn 1367 3793 a(@) p Fl 1415 3807 a(1) p Fn 1455 3793 a(P) p Fp 1551 3793 a(=) p Fn 1647 3793 a(P) p Fp 1718 3793 a(\() p Fn(@) p Fl 1801 3807 a(1) p Fn 1841 3793 a(P) p Fp 1912 3793 a(\)) p Fn(Q) p Fp 2040 3793 a(+) p Fn 2131 3793 a(Q) p Fp(\() p Fn(@) p Fl 2286 3807 a(1) p Fn 2326 3793 a(P) p Fp 2397 3793 a(\)) p Fn(P) s(;) 448 4009 y @beginspecial @setspecial @endspecial Fo(wher) p 629 4009 a(e) p Fn 705 4009 a(Q) p Fp 802 4009 a(:=) p 923 4009 a(1) p Fh 989 4009 a(\000) p Fn 1080 4009 a(P) p Fo 1151 4009 a(.) 448 4258 y @beginspecial @setspecial @endspecial(Pr) p 543 4258 a(o) p 584 4258 a(of.) p Fp 728 4258 a(Since) p Fn 965 4258 a(P) p Fl 1036 4225 a(2) p Fp 1101 4258 a(=) p Fn 1197 4258 a(P) p Fp 1268 4258 a(,) p 1324 4258 a(w) m(e) p 1458 4258 a(ha) m(v) m(e) 847 4474 y(\() p Fn(@) p Fl 930 4488 a(1) p Fn 970 4474 a(P) p Fp 1041 4474 a(\)\() p Fn(!) p Fp 1187 4474 a(;) p Fn 1227 4474 a(x;) p 1319 4474 a(y) p Fp 1367 4474 a(\)) p 1428 4474 a(=) p Fi 1553 4393 a(X) p Fj 1524 4591 a(z) p Fm 1560 4591 a(2) p Fg(Z) p 1623 4591 a(Z) p Ff 1665 4566 a(d) p Fp 1702 4474 a(\() p Fn(x) p Fl 1789 4488 a(1) p Fh 1849 4474 a(\000) p Fn 1939 4474 a(z) p Fl 1981 4488 a(1) p Fp 2021 4474 a(\)) p Fn(P) p Fp 2127 4474 a(\() p Fn(!) p Fp 2238 4474 a(;) p Fn 2278 4474 a(x;) p 2370 4474 a(z) p Fp 2416 4474 a(\)) p Fn(P) p Fp 2522 4474 a(\() p Fn(!) p Fp 2634 4474 a(;) p Fn 2674 4474 a(z) t(;) p 2760 4474 a(y) p Fp 2808 4474 a(\)) 1615 4726 y(+) p Fi 1730 4645 a(X) p Fj 1701 4844 a(z) p Fm 1737 4844 a(2) p Fg(Z) p 1800 4844 a(Z) p Ff 1842 4818 a(d) p Fp 1878 4726 a(\() p Fn(z) p Fl 1955 4740 a(1) p Fh 2016 4726 a(\000) p Fn 2107 4726 a(y) p Fl 2152 4740 a(1) p Fp 2191 4726 a(\)) p Fn(P) p Fp 2297 4726 a(\() p Fn(!) p Fp 2407 4726 a(;) p Fn 2447 4726 a(x;) p 2539 4726 a(z) p Fp 2585 4726 a(\)) p Fn(P) p Fp 2691 4726 a(\() p Fn(!) p Fp 2803 4726 a(;) p Fn 2843 4726 a(z) t(;) p 2929 4726 a(y) p Fp 2977 4726 a(\)) p Fn(:) p Fp 1897 5225 a(29) p eop %%Page: 30 30 30 29 bop 448 573 a @beginspecial @setspecial @endspecial Fp(Since) p Fn 683 573 a(@) p Fl 731 587 a(1) p Fn 771 573 a(P) p Fh 867 573 a(2) p 953 573 a(L) p Fl 1016 540 a(2) p Fp 1055 573 a(,) p 1108 573 a(the) p 1262 573 a(sums) p 1487 573 a(in) p 1590 573 a(the) p 1744 573 a(ab) s(o) m(v) m(e) p 1999 573 a(expression) p 2434 573 a(are) p 2583 573 a(absolutely) p 3013 573 a(con) m(v) m(ergen) m (t) 448 697 y(\(Lemma) p 815 697 a(2.1\).) p 1054 697 a(Hence,) p 1359 697 a(as) p 1478 697 a(elemen) m(ts) p 1857 697 a(of) p Fh 1968 697 a(L) p Fl 2031 664 a(2) p Fp 2070 697 a(,) p Fn 2134 697 a(@) p Fl 2182 711 a(1) p Fn 2222 697 a(P) p Fp 2331 697 a(=) p 2439 697 a(\() p Fn(@) p Fl 2522 711 a(1) p Fn 2562 697 a(P) p Fp 2633 697 a(\)) p Fn(P) p Fp 2764 697 a(+) p Fn 2860 697 a(P) p Fp 2931 697 a(\() p Fn(@) p Fl 3014 711 a(1) p Fn 3054 697 a(P) p Fp 3125 697 a(\).) p 3248 697 a(Mul-) 448 822 y(tiplying) p Fn 790 822 a(P) p Fp 897 822 a(and) p Fn 1079 822 a(Q) p Fp 1187 822 a(from) p 1408 822 a(b) s(oth) p 1628 822 a(sides,) p 1879 822 a(w) m(e) p 2018 822 a(ha) m(v) m(e) p Fn 2233 822 a(P) p Fp 2304 822 a(\() p Fn(@) p Fl 2387 836 a(1) p Fn 2427 822 a(P) p Fp 2498 822 a(\)) p Fn(P) p Fp 2640 822 a(=) p 2745 822 a(0,) p Fn 2853 822 a(Q) p Fp(\() p Fn(@) p Fl 3008 836 a(1) p Fn 3048 822 a(P) p Fp 3119 822 a(\)) p Fn(Q) p Fp 3261 822 a(=) p 3366 822 a(0.) 448 946 y(Therefore,) p Fn 1363 1162 a(@) p Fl 1411 1176 a(1) p Fn 1451 1162 a(P) p Fp 1547 1162 a(=) p 1643 1162 a(\() p Fn(P) p Fp 1770 1162 a(+) p Fn 1861 1162 a(Q) p Fp(\)\() p Fn(@) p Fl 2051 1176 a(1) p Fn 2091 1162 a(P) p Fp 2162 1162 a(\)\() p Fn(P) p Fp 2324 1162 a(+) p Fn 2415 1162 a(Q) p Fp(\)) 1547 1312 y(=) p Fn 1643 1312 a(P) p Fp 1714 1312 a(\() p Fn(@) p Fl 1797 1326 a(1) p Fn 1837 1312 a(P) p Fp 1908 1312 a(\)) p Fn(Q) p Fp 2036 1312 a(+) p Fn 2127 1312 a(Q) p Fp(\() p Fn(@) p Fl 2282 1326 a(1) p Fn 2322 1312 a(P) p Fp 2393 1312 a(\)) p Fn(P) s(:) p 448 1464 60 4 v 448 1553 4 89 v 504 1553 V 448 1556 60 4 v Fe 448 1777 a(Lemma) p 819 1777 a(3.5) p 998 1777 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1094 1777 a(A) p Fh 1187 1777 a(2) p 1273 1777 a(D) p Fp 1346 1777 a(\() p Fh(L) p Fj 1444 1791 a(H) p Ff 1502 1799 a(!) p Fp 1550 1777 a(\)) p Fo(,) p 1646 1777 a(then) p Fn 1848 1777 a(P) p 1919 1777 a(AQ) p Fh 2085 1777 a(2) p 2170 1777 a(D) p Fp 2243 1777 a(\() p Fh(L) p Fj 2341 1791 a(H) p Ff 2399 1799 a(!) p Fp 2448 1777 a(\)) p Fo(,) p 2544 1777 a(and) p 2720 1777 a(we) p 2855 1777 a(have) p Fh 1418 1993 a(L) p Fj 1481 2007 a(H) p Ff 1539 2015 a(!) p Fp 1588 1993 a(\() p Fn(P) p 1694 1993 a(AQ) p Fp(\)) p 1895 1993 a(=) p Fn 1991 1993 a(P) p Fh 2062 1993 a(L) p Fj 2125 2007 a(H) p Ff 2183 2015 a(!) p Fp 2231 1993 a(\() p Fn(A) p Fp(\)) p Fn(Q:) p Fe 448 2433 a(Remark) p 846 2433 a(3.3) p 1025 2433 a @beginspecial @setspecial @endspecial Fo(By) p 1165 2433 a(Pr) p 1260 2433 a(op) p 1347 2433 a(osition) p 1649 2433 a(2.5,) p Fn 1830 2433 a(P) p 1901 2433 a(AQ) p Fh 2066 2433 a(2) p 2152 2433 a(L) p Fl 2215 2400 a(2) p Fo 2254 2433 a(.) p Fh 2324 2433 a(L) p Fj 2387 2447 a(H) p Ff 2445 2455 a(!) p Fp 2493 2433 a(\() p Fn(P) p 2599 2433 a(AQ) p Fp(\)) p Fo 2808 2433 a(is) p 2905 2433 a(de\014ne) p 3132 2433 a(d) p 3212 2433 a(as) p Fh 1113 2648 a(L) p Fj 1176 2662 a(H) p Ff 1234 2670 a(!) p Fp 1283 2648 a(\() p Fn(P) p 1389 2648 a(AQ) p Fp(\)) p 1590 2648 a(:=) p Fn(<) p 1782 2648 a(\016) p Fj 1822 2662 a(x) p Fn 1866 2648 a(;) p Fp 1906 2648 a([) p Fn(H) p Fj 2007 2662 a(!) p Fn 2057 2648 a(;) p 2097 2648 a(P) p 2168 2648 a(AQ) p Fp(]) p Fn(\016) p Fj 2373 2662 a(y) p Fn 2441 2648 a(>) p Fj 2512 2677 a(l) p Fc 2534 2658 a(2) p Fl 2568 2677 a(\() p Fg(Z) p 2610 2677 a(Z) p Ff 2654 2652 a(d) p Fl 2690 2677 a(\)) p Fn 2747 2648 a(:) 448 2864 y(h) p Fp 534 2864 a(:=) p Fn 663 2864 a(\031) p Fp 718 2864 a(\() p Fn(H) p Fj 829 2878 a(!) p Fp 879 2864 a(\)) p Fo 951 2864 a(satis\014es) p Fn 1297 2864 a(h) p Fp(\() p Fn(!) s(;) p 1484 2864 a(x) p Fp(\)) p 1606 2864 a(=) p 1709 2864 a(0) p Fo(,) p 1821 2864 a(if) p Fh 1913 2864 a(j) p Fn(x) p Fh(j) p 2049 2864 a(\025) p Fp 2153 2864 a(2) p Fo(,) p 2264 2864 a(and) p Fn 2445 2864 a(h) p Fp(\() p Fn(!) s(;) p 2632 2864 a(x) p Fp(\)) p Fn 2753 2864 a(<) p Fh 2857 2864 a(1) p Fo(.) p 3031 2864 a(Ther) p 3217 2864 a(efor) p 3366 2864 a(e,) p Fn 448 2989 a(<) p 569 2989 a(\016) p Fj 609 3003 a(x) p Fn 654 2989 a(;) p Fp 694 2989 a([) p Fn(H) p Fj 795 3003 a(!) p Fn 845 2989 a(;) p 885 2989 a(P) p 956 2989 a(AQ) p Fp(]) p Fn(\016) p Fj 1161 3003 a(y) p Fn 1254 2989 a(>) p Fj 1325 3018 a(l) p Fc 1347 2999 a(2) p Fl 1381 3018 a(\() p Fg(Z) p 1423 3018 a(Z) p Ff 1467 2992 a(d) p Fl 1503 3018 a(\)) p Fo 1581 2989 a(makes) p 1869 2989 a(sense.) p 2189 2989 a(We) p 2368 2989 a(note) p 2584 2989 a(that) p Fn 2784 2989 a(A) p Fh 2902 2989 a(2) p 3013 2989 a(D) p Fp 3086 2989 a(\() p Fh(L) p Fj 3184 3003 a(H) p Ff 3242 3011 a(!) p Fp 3290 2989 a(\)) p Fo 3372 2989 a(is) 448 3113 y(e) p 485 3113 a(quivalent) p 874 3113 a(to) p 987 3113 a(the) p 1141 3113 a(statement) p 1560 3113 a(that) p Fh 1749 3113 a(L) p Fj 1812 3127 a(V) p Ff 1853 3135 a(!) p Fp 1902 3113 a(\() p Fn(A) p Fp(\)\() p Fn(!) p Fp 2151 3113 a(;) p Fn 2191 3113 a(x;) p 2283 3113 a(y) p Fp 2331 3113 a(\)) p 2398 3113 a(:=) p Fn(<) p 2596 3113 a(\016) p Fj 2636 3127 a(x) p Fn 2680 3113 a(;) p Fp 2720 3113 a([) p Fn(V) p Fj 2798 3127 a(!) p Fn 2849 3113 a(;) p 2889 3113 a(A) p Fp(]) p Fn(\016) p Fj 3022 3127 a(y) p Fn 3096 3113 a(>) p Fj 3167 3142 a(l) p Fc 3189 3123 a(2) p Fl 3223 3142 a(\() p Fg(Z) p 3265 3142 a(Z) p Ff 3309 3117 a(d) p Fl 3345 3142 a(\)) p Fh 3377 3113 a(2) 448 3238 y(L) p Fl 511 3205 a(2) p Fo 550 3238 a(.) 448 3487 y @beginspecial @setspecial @endspecial(Pr) p 543 3487 a(o) p 584 3487 a(of.) p Fp 728 3487 a(Let) p Fn 891 3487 a(a) p Fp 964 3487 a(:=) p Fn 1086 3487 a(\031) p Fp 1141 3487 a(\() p Fn(A) p Fp(\),) p 1335 3487 a(and) p 1512 3487 a(de\014ne) p Fn 865 3734 a(a) p Fj 913 3748 a(n) p Fp 960 3734 a(\() p Fn(!) s(;) p 1095 3734 a(x) p Fp(\)) p 1208 3734 a(:=) p Fi 1329 3615 a(\032) p Fn 1406 3677 a(a) p Fp(\() p Fn(!) s(;) p 1589 3677 a(x) p Fp(\)) p Fn(;) p Fp 1794 3677 a(\(if) p Fh 1912 3677 a(j) p Fn(x) p Fh(j) p 2040 3677 a(\024) p Fn 2136 3677 a(n) p Fp(,) p 2246 3677 a(and) p Fh 2423 3677 a(j) p Fn(a) p Fp(\() p Fn(!) s(;) p 2631 3677 a(x) p Fp(\)) p Fh(j) p 2769 3677 a(\024) p Fn 2865 3677 a(n) p Fp(\),) 1406 3790 y(0) p Fn(;) p Fp 1794 3790 a(\(otherwise\).) 448 3989 y @beginspecial @setspecial @endspecial(Then,) p Fn 715 3989 a(A) p Fj 783 4003 a(n) p Fp 860 3989 a(:=) p Fn 986 3989 a(\031) p Fm 1041 3956 a(\000) p Fl(1) p Fp 1136 3989 a(\() p Fn(a) p Fj 1219 4003 a(n) p Fp 1266 3989 a(\)) p Fh 1332 3989 a(!) p Fn 1453 3989 a(A) p Fp 1555 3989 a(in) p Fh 1664 3989 a(L) p Fl 1727 3956 a(2) p Fp 1766 3989 a(.) p 1841 3989 a(Since) p Fh 2081 3989 a(L) p Fj 2144 4003 a(V) p Ff 2185 4011 a(!) p Fp 2234 3989 a(\() p Fn(A) p Fp(\)) p Fh 2403 3989 a(2) p 2494 3989 a(L) p Fl 2557 3956 a(2) p Fp 2596 3989 a(,) p Fh 2655 3989 a(L) p Fj 2718 4003 a(V) p Ff 2759 4011 a(!) p Fp 2808 3989 a(\() p Fn(A) p Fj 2911 4003 a(n) p Fp 2959 3989 a(\)) p Fh 3024 3989 a(!) p 3145 3989 a(L) p Fj 3208 4003 a(V) p Ff 3249 4011 a(!) p Fp 3298 3989 a(\() p Fn(A) p Fp(\)) 448 4113 y(in) p Fh 562 4113 a(L) p Fl 625 4080 a(2) p Fp 702 4113 a(as) p Fn 822 4113 a(n) p Fh 914 4113 a(!) p 1043 4113 a(1) p Fp(.) p 1223 4113 a(W) p 1308 4113 a(e) p 1388 4113 a(write) p Fn 1628 4113 a(H) p Fj 1704 4127 a(!) p Fp 1792 4113 a(=) p Fn 1901 4113 a(H) p Fl 1977 4127 a(0) p Fp 2041 4113 a(+) p Fn 2137 4113 a(V) p Fj 2190 4127 a(!) p Fp 2241 4113 a(.) p 2330 4113 a(Since) p Fn 2575 4113 a(H) p Fl 2651 4127 a(0) p Fp 2690 4113 a(,) p Fn 2755 4113 a(P) p Fp 2826 4113 a(,) p Fn 2891 4113 a(Q) p Fp(,) p Fn 3028 4113 a(A) p Fj 3096 4127 a(n) p Fp 3182 4113 a(are) p 3341 4113 a(all) 448 4238 y(b) s(ounded) p 820 4238 a(on) p Fn 946 4238 a(l) p Fl 975 4205 a(2) p Fp 1014 4238 a(\() p Fk(Z) p 1069 4238 a(Z) p Fj 1124 4201 a(d) p Fp 1165 4238 a(\),) p Fh 874 4453 a(L) p Fj 937 4467 a(H) p Fc 995 4476 a(0) p Fp 1034 4453 a(\() p Fn(P) p 1140 4453 a(A) p Fj 1208 4467 a(n) p Fn 1255 4453 a(Q) p Fp(\)\() p Fn(!) p Fp 1473 4453 a(;) p Fn 1513 4453 a(x;) p 1605 4453 a(y) p Fp 1653 4453 a(\)) p 448 4453 a(\(3.10\)) 1034 4603 y(=) p 1130 4603 a(\() p Fh(L) p Fj 1228 4617 a(H) p Fc 1286 4626 a(0) p Fp 1324 4603 a(\() p Fn(P) p Fp 1430 4603 a(\)) p Fn(A) p Fj 1533 4617 a(n) p Fn 1581 4603 a(Q) p Fp(\)\() p Fn(!) p Fp 1799 4603 a(;) p Fn 1839 4603 a(x;) p 1931 4603 a(y) p Fp 1979 4603 a(\)) p 2035 4603 a(+) p 2126 4603 a(\() p Fn(P) p Fh 2232 4603 a(L) p Fj 2295 4617 a(H) p Fc 2353 4626 a(0) p Fp 2392 4603 a(\() p Fn(A) p Fj 2495 4617 a(n) p Fp 2542 4603 a(\)) p Fn(Q) p Fp(\)\() p Fn(!) p Fp 2795 4603 a(;) p Fn 2835 4603 a(x;) p 2927 4603 a(y) p Fp 2975 4603 a(\)) 1125 4752 y(+\() p Fn(P) p 1302 4752 a(A) p Fj 1370 4766 a(n) p Fh 1417 4752 a(L) p Fj 1480 4766 a(H) p Fc 1538 4775 a(0) p Fp 1576 4752 a(\() p Fn(Q) p Fp(\)\)\() p Fn(!) p Fp 1865 4752 a(;) p Fn 1905 4752 a(x;) p 1997 4752 a(y) p Fp 2045 4752 a(\)) p Fn(:) p Fp 1897 5225 a(30) p eop %%Page: 31 31 31 30 bop 448 573 a @beginspecial @setspecial @endspecial Fp(On) p 600 573 a(the) p 756 573 a(other) p 994 573 a(hand,) p Fh 737 755 a(L) p Fj 800 769 a(V) p Ff 841 777 a(!) p Fp 889 755 a(\() p Fn(P) p 995 755 a(A) p Fj 1063 769 a(n) p Fn 1111 755 a(Q) p Fp(\)\() p Fn(!) p Fp 1328 755 a(;) p Fn 1368 755 a(x;) p 1460 755 a(y) p Fp 1508 755 a(\)) p 448 755 a(\(3.11\)) 889 905 y(=) p Fi 1074 824 a(X) p Fj 985 1023 a(z) p Fc 1018 1032 a(1) p Fj 1053 1023 a(;z) p Fc 1106 1032 a(2) p Fm 1140 1023 a(2) p Fg(Z) p 1203 1023 a(Z) p Ff 1246 997 a(d) p Fn 1297 905 a(P) p Fp 1368 905 a(\() p Fn(!) p Fp 1478 905 a(;) p Fn 1518 905 a(x;) p 1610 905 a(z) p Fl 1652 919 a(1) p Fp 1693 905 a(\)) p Fn(A) p Fj 1796 919 a(n) p Fp 1843 905 a(\() p Fn(!) p Fp 1954 905 a(;) p Fn 1994 905 a(z) p Fl 2036 919 a(1) p Fn 2076 905 a(;) p 2116 905 a(z) p Fl 2158 919 a(2) p Fp 2198 905 a(\)) p Fn(Q) p Fp(\() p Fn(!) p Fp 2416 905 a(;) p Fn 2456 905 a(z) p Fl 2498 919 a(2) p Fn 2538 905 a(;) p 2578 905 a(y) p Fp 2626 905 a(\)) p Fh 2681 905 a(\002) 980 1145 y(\002) p Fp(\() p Fn(V) p Fj 1139 1159 a(!) p Fp 1190 1145 a(\() p Fn(x) p Fp(\)) p Fh 1333 1145 a(\000) p Fn 1424 1145 a(V) p Fj 1477 1159 a(!) p Fp 1527 1145 a(\() p Fn(z) p Fl 1604 1159 a(1) p Fp 1644 1145 a(\)) p 1700 1145 a(+) p Fn 1791 1145 a(V) p Fj 1844 1159 a(!) p Fp 1894 1145 a(\() p Fn(z) p Fl 1971 1159 a(1) p Fp 2011 1145 a(\)) p Fh 2067 1145 a(\000) p Fn 2158 1145 a(V) p Fj 2211 1159 a(!) p Fp 2261 1145 a(\() p Fn(z) p Fl 2338 1159 a(2) p Fp 2378 1145 a(\)) p 2434 1145 a(+) p Fn 2524 1145 a(V) p Fj 2577 1159 a(!) p Fp 2628 1145 a(\() p Fn(z) p Fl 2705 1159 a(2) p Fp 2745 1145 a(\)) p Fh 2801 1145 a(\000) p Fn 2891 1145 a(V) p Fj 2944 1159 a(!) p Fp 2995 1145 a(\() p Fn(y) p Fp 3078 1145 a(\)\)) 889 1295 y(=) p 985 1295 a(\() p Fh(L) p Fj 1083 1309 a(V) p Ff 1124 1317 a(!) p Fp 1173 1295 a(\() p Fn(P) p Fp 1279 1295 a(\)) p Fn(A) p Fj 1382 1309 a(n) p Fn 1430 1295 a(Q) p Fp(\)\() p Fn(!) p Fp 1648 1295 a(;) p Fn 1688 1295 a(x;) p 1780 1295 a(y) p Fp 1828 1295 a(\)) p 1884 1295 a(+) p 1975 1295 a(\() p Fn(P) p Fh 2081 1295 a(L) p Fj 2144 1309 a(V) p Ff 2185 1317 a(!) p Fp 2234 1295 a(\() p Fn(A) p Fj 2337 1309 a(n) p Fp 2384 1295 a(\)) p Fn(Q) p Fp(\)\() p Fn(!) p Fp 2637 1295 a(;) p Fn 2677 1295 a(x;) p 2769 1295 a(y) p Fp 2817 1295 a(\)) 980 1444 y(+\() p Fn(P) p 1157 1444 a(A) p Fj 1225 1458 a(n) p Fh 1272 1444 a(L) p Fj 1335 1458 a(V) p Ff 1376 1466 a(!) p Fp 1425 1444 a(\() p Fn(Q) p Fp(\)\)\() p Fn(!) p Fp 1714 1444 a(;) p Fn 1754 1444 a(x;) p 1846 1444 a(y) p Fp 1894 1444 a(\)) p Fn(:) 448 1627 y @beginspecial @setspecial @endspecial Fp(Since) p Fn 676 1627 a(A) p Fp(,) p Fn 793 1627 a(P) p Fh 889 1627 a(2) p 975 1627 a(D) p Fp 1048 1627 a(\() p Fh(L) p Fj 1146 1641 a(H) p Ff 1204 1649 a(!) p Fp 1252 1627 a(\),) p 1336 1627 a(the) p 1483 1627 a(sums) p 1702 1627 a(app) s(earing) p 2114 1627 a(in) p 2211 1627 a(the) p 2358 1627 a(ab) s(o) m(v) m(e) p 2606 1627 a(expression) p 3035 1627 a(absolutely) 448 1751 y(con) m(v) m(erge.) p 853 1751 a(By) p 991 1751 a(\(3.10\),) p 1275 1751 a(\(3.11\),) p 1559 1751 a(and) p 1730 1751 a(the) p 1882 1751 a(equalit) m(y) p Fh 2222 1751 a(L) p Fj 2285 1765 a(H) p Ff 2343 1773 a(!) p Fp 2392 1751 a(\() p Fn(P) p Fp 2498 1751 a(\)) p 2559 1751 a(=) p Fh 2655 1751 a(L) p Fj 2718 1765 a(H) p Fc 2776 1774 a(0) p Fp 2814 1751 a(\() p Fn(P) p Fp 2920 1751 a(\)) p 2965 1751 a(+) p Fh 3046 1751 a(L) p Fj 3109 1765 a(V) p Ff 3150 1773 a(!) p Fp 3199 1751 a(\() p Fn(P) p Fp 3305 1751 a(\)) p 3366 1751 a(=) 448 1876 y(0,) p 549 1876 a(w) m(e) p 683 1876 a(ha) m(v) m(e) p Fh 1371 2000 a(L) p Fj 1434 2014 a(H) p Ff 1492 2022 a(!) p Fp 1541 2000 a(\() p Fn(P) p 1647 2000 a(A) p Fj 1715 2014 a(n) p Fn 1762 2000 a(Q) p Fp(\)) p 1895 2000 a(=) p Fn 1991 2000 a(P) p Fh 2062 2000 a(L) p Fj 2125 2014 a(H) p Ff 2183 2022 a(!) p Fp 2231 2000 a(\() p Fn(A) p Fj 2334 2014 a(n) p Fp 2382 2000 a(\)) p Fn(Q:) p Fp 448 2000 a(\(3.12\)) p Fn 448 2162 a(P) p Fh 519 2162 a(L) p Fj 582 2176 a(H) p Ff 640 2184 a(!) p Fp 689 2162 a(\() p Fn(A) p Fj 792 2176 a(n) p Fp 839 2162 a(\)) p Fn(Q) p Fh 972 2162 a(!) p Fn 1088 2162 a(P) p Fh 1159 2162 a(L) p Fj 1222 2176 a(H) p Ff 1280 2184 a(!) p Fp 1329 2162 a(\() p Fn(A) p Fp(\)) p Fn(Q) p Fp 1570 2162 a(in) p Fh 1676 2162 a(L) p Fl 1739 2129 a(2) p Fp 1808 2162 a(\() p Fn(n) p Fh 1923 2162 a(!) p 2040 2162 a(1) p Fp(\),) p 2221 2162 a(and) p 2398 2162 a(b) m(y) p 2524 2162 a(taking) p 2805 2162 a(subsequence,) 988 2345 y(\() p Fn(P) p Fh 1094 2345 a(L) p Fj 1157 2359 a(H) p Ff 1215 2367 a(!) p Fp 1263 2345 a(\() p Fn(A) p Fj 1366 2359 a(n) p Fp 1414 2345 a(\)) p Fn(Q) p Fp(\)\() p Fn(!) p Fp 1667 2345 a(;) p Fn 1707 2345 a(x;) p 1799 2345 a(y) p Fp 1847 2345 a(\)) p Fh 1908 2345 a(!) p Fp 2024 2345 a(\() p Fn(P) p Fh 2130 2345 a(L) p Fj 2193 2359 a(H) p Ff 2251 2367 a(!) p Fp 2300 2345 a(\() p Fn(A) p Fp(\)) p Fn(Q) p Fp(\)\() p Fn(!) p Fp 2657 2345 a(;) p Fn 2697 2345 a(x;) p 2789 2345 a(y) p Fp 2837 2345 a(\)) p Fn(;) p Fp 448 2345 a(\(3.13\)) 448 2527 y @beginspecial @setspecial @endspecial(as) p Fn 563 2527 a(n) p Fh 648 2527 a(!) p 769 2527 a(1) p Fp 894 2527 a(for) p 1036 2527 a(a.e.) p Fn 1222 2527 a(!) p Fp 1282 2527 a(,) p 1341 2527 a(and) p 1521 2527 a(for) p 1664 2527 a(an) m(y) p Fn 1838 2527 a(x) p Fp(,) p Fn 1950 2527 a(y) p Fh 2028 2527 a(2) p Fk 2119 2527 a(Z) p 2139 2527 a(Z) p Fj 2194 2491 a(d) p Fp 2234 2527 a(.) p 2309 2527 a(On) p 2464 2527 a(the) p 2624 2527 a(other) p 2864 2527 a(hand,) p 3121 2527 a(w) m(e) p 3258 2527 a(ha) m(v) m(e) 448 2652 y(\() p Fn(P) p 554 2652 a(A) p Fj 622 2666 a(n) p Fn 670 2652 a(Q) p Fp(\)\() p Fn(!) p Fp 887 2652 a(;) p Fn 927 2652 a(x;) p 1019 2652 a(y) p Fp 1067 2652 a(\)) p Fh 1147 2652 a(!) p Fp 1281 2652 a(\() p Fn(P) p 1387 2652 a(AQ) p Fp(\)\() p Fn(!) p Fp 1673 2652 a(;) p Fn 1713 2652 a(x;) p 1805 2652 a(y) p Fp 1853 2652 a(\),) p 1959 2652 a(as) p Fn 2081 2652 a(n) p Fh 2179 2652 a(!) p 2314 2652 a(1) p Fp 2446 2652 a(for) p 2596 2652 a(a.e.) p Fn 2806 2652 a(!) p Fp 2866 2652 a(,) p 2935 2652 a(b) m(y) p 3072 2652 a(the) p 3240 2652 a(same) 448 2776 y(reason.) p 767 2776 a(Since) p Fn 1005 2776 a(h) p Fp(\() p Fn(!) s(;) p 1192 2776 a(x) p Fp(\)) p 1305 2776 a(=) p 1401 2776 a(0) p 1477 2776 a(if) p Fh 1560 2776 a(j) p Fn(x) p Fh(j) p 1688 2776 a(\025) p Fp 1784 2776 a(2,) p 1885 2776 a(and) p Fh 2062 2776 a(j) p Fn(h) p Fp(\() p Fn(!) s(;) p 2274 2776 a(x) p Fp(\)) p Fh(j) p Fn 2413 2776 a(<) p Fh 2509 2776 a(1) p Fp 2630 2776 a(for) p 2769 2776 a(a.e.) p Fn 2946 2776 a(!) p Fp 3006 2776 a(,) p Fh 1071 2959 a(L) p Fj 1134 2973 a(H) p Ff 1192 2981 a(!) p Fp 1240 2959 a(\() p Fn(P) p 1346 2959 a(A) p Fj 1414 2973 a(n) p Fn 1462 2959 a(Q) p Fp(\)\() p Fn(!) p Fp 1680 2959 a(;) p Fn 1720 2959 a(x;) p 1812 2959 a(y) p Fp 1860 2959 a(\)) p Fh 1921 2959 a(!) p 2037 2959 a(L) p Fj 2100 2973 a(H) p Ff 2158 2981 a(!) p Fp 2207 2959 a(\() p Fn(P) p 2313 2959 a(AQ) p Fp(\)\() p Fn(!) p Fp 2599 2959 a(;) p Fn 2639 2959 a(x;) p 2731 2959 a(y) p Fp 2779 2959 a(\)) p 448 2959 a(\(3.14\)) 448 3142 y @beginspecial @setspecial @endspecial(for) p 601 3142 a(a.e.) p Fn 817 3142 a(!) p Fp 877 3142 a(,) p 949 3142 a(as) p Fn 1074 3142 a(n) p Fh 1175 3142 a(!) p 1313 3142 a(1) p Fp(.) p 1510 3142 a(By) p 1665 3142 a(\(3.12\),) p 1970 3142 a(\(3.13\),) p 2274 3142 a(and) p 2464 3142 a(\(3.14\),) p 2768 3142 a(w) m(e) p 2915 3142 a(arriv) m(e) p 3187 3142 a(at) p 3311 3142 a(the) 448 3266 y(conclusion.) p 924 3202 60 4 v 924 3291 4 89 v 979 3291 V 924 3294 60 4 v Fe 448 3515 a(Lemma) p 819 3515 a(3.6) p 998 3515 a @beginspecial @setspecial @endspecial Fn 833 3698 a(Q) p Fh(f) p Fp(\() p Fh(\000) p Fn(i\016) p Fh 1152 3698 a(\000) p 1243 3698 a(L) p Fj 1306 3712 a(H) p Ff 1364 3720 a(!) p Fp 1412 3698 a(\)) p Fm 1447 3660 a(\000) p Fl(1) p Fn 1542 3698 a(@) p Fl 1590 3712 a(1) p Fn 1630 3698 a(H) p Fj 1706 3712 a(!) p Fh 1756 3698 a(g) p Fn(P) p Fp 1897 3698 a(=) p 1993 3698 a(\() p Fh(\000) p Fn(i\016) p Fh 2195 3698 a(\000) p 2286 3698 a(L) p Fj 2349 3712 a(H) p Ff 2407 3720 a(!) p Fp 2455 3698 a(\)) p Fm 2490 3660 a(\000) p Fl(1) p Fp 2585 3698 a(\() p Fn(Q@) p Fl 2740 3712 a(1) p Fn 2780 3698 a(H) p Fj 2856 3712 a(!) p Fn 2906 3698 a(P) p Fp 2977 3698 a(\)) p Fn(;) p Fp 448 3698 a(\(3.15\)) p Fn 848 3847 a(P) p Fh 919 3847 a(f) p Fp(\() p Fh(\000) p Fn(i\016) p Fh 1166 3847 a(\000) p 1257 3847 a(L) p Fj 1320 3861 a(H) p Ff 1378 3869 a(!) p Fp 1426 3847 a(\)) p Fm 1461 3810 a(\000) p Fl(1) p Fn 1556 3847 a(@) p Fl 1604 3861 a(1) p Fn 1644 3847 a(H) p Fj 1720 3861 a(!) p Fh 1770 3847 a(g) p Fn(Q) p Fp 1912 3847 a(=) p 2008 3847 a(\() p Fh(\000) p Fn(i\016) p Fh 2210 3847 a(\000) p 2301 3847 a(L) p Fj 2364 3861 a(H) p Ff 2422 3869 a(!) p Fp 2470 3847 a(\)) p Fm 2505 3810 a(\000) p Fl(1) p Fp 2600 3847 a(\() p Fn(P) p 2706 3847 a(@) p Fl 2754 3861 a(1) p Fn 2794 3847 a(H) p Fj 2870 3861 a(!) p Fn 2920 3847 a(Q) p Fp(\)) p Fn(:) p Fp 448 3847 a(\(3.16\)) 448 4279 y @beginspecial @setspecial @endspecial Fo(Pr) p 543 4279 a(o) p 584 4279 a(of.) p Fp 728 4279 a(Let) p Fn 738 4462 a(A) p Fp 832 4462 a(:=) p Fn 953 4462 a(Q) p Fh(f) p Fp(\() p Fh(\000) p Fn(i\016) p Fh 1272 4462 a(\000) p 1363 4462 a(L) p Fj 1426 4476 a(H) p Ff 1484 4484 a(!) p Fp 1532 4462 a(\)) p Fm 1567 4424 a(\000) p Fl(1) p Fn 1662 4462 a(@) p Fl 1710 4476 a(1) p Fn 1750 4462 a(H) p Fj 1826 4476 a(!) p Fh 1876 4462 a(g) p Fn(P) p Fh 2012 4462 a(\000) p Fp 2103 4462 a(\() p Fh(\000) p Fn(i\016) p Fh 2304 4462 a(\000) p 2395 4462 a(L) p Fj 2458 4476 a(H) p Ff 2516 4484 a(!) p Fp 2565 4462 a(\)) p Fm 2600 4424 a(\000) p Fl(1) p Fp 2695 4462 a(\() p Fn(Q@) p Fl 2850 4476 a(1) p Fn 2890 4462 a(H) p Fj 2966 4476 a(!) p Fn 3016 4462 a(P) p Fp 3087 4462 a(\)) p Fn(:) 448 4644 y @beginspecial @setspecial @endspecial Fp(The) p 635 4644 a(\014rst) p 823 4644 a(term) p 1040 4644 a(of) p 1144 4644 a(RHS) p 1360 4644 a(b) s(elongs) p 1686 4644 a(to) p Fh 1797 4644 a(D) p Fp 1870 4644 a(\() p Fh(L) p Fj 1968 4658 a(H) p Ff 2026 4666 a(!) p Fp 2075 4644 a(\)) p 2140 4644 a(b) m(y) p 2267 4644 a(Lemma) p 2591 4644 a(3.5.) p 2773 4644 a(Moreo) m(v) m(er,) 1117 4827 y(\() p Fh(\000) p Fn(i\016) p Fh 1318 4827 a(\000) p 1409 4827 a(L) p Fj 1472 4841 a(H) p Ff 1530 4849 a(!) p Fp 1579 4827 a(\)) p Fn(A) p Fp 1707 4827 a(=) p Fn 1803 4827 a(Q) p Fp(\() p Fn(@) p Fl 1958 4841 a(1) p Fn 1998 4827 a(H) p Fj 2074 4841 a(!) p Fp 2124 4827 a(\)) p Fn(P) p Fh 2251 4827 a(\000) p Fn 2342 4827 a(Q) p Fp(\() p Fn(@) p Fl 2497 4841 a(1) p Fn 2537 4827 a(H) p Fj 2613 4841 a(!) p Fp 2663 4827 a(\)) p Fn(P) p Fp 1707 4976 a(=) p 1803 4976 a(0) p Fn(:) p Fp 1897 5225 a(31) p eop %%Page: 32 32 32 31 bop 448 573 a @beginspecial @setspecial @endspecial Fp(Therefore,) p Fn 886 573 a(A) p Fp 979 573 a(=) p 1075 573 a(0.) p 1186 573 a(The) p 1373 573 a(pro) s(of) p 1611 573 a(of) p 1714 573 a(\(3.16\)) p 1977 573 a(is) p 2068 573 a(similar.) p 2402 509 60 4 v 2402 598 4 89 v 2458 598 V 2402 601 60 4 v Fe 448 822 a(Lemma) p 819 822 a(3.7) p 998 822 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1094 822 a(P) p Fh 1190 822 a(2) p 1276 822 a(D) p Fp 1349 822 a(\() p Fn(@) p Fl 1432 836 a(1) p Fp 1471 822 a(\)) p Fo(,) p 1567 822 a(then) p Fp 1769 822 a(\() p Fn(Qx) p Fl 1928 836 a(1) p Fn 1968 822 a(P) p Fp 2039 822 a(\)\() p Fn(!) p Fp 2185 822 a(;) p Fn 2225 822 a(x;) p 2317 822 a(y) p Fp 2365 822 a(\)) p Fo 2433 822 a(is) p 2531 822 a(\014nite) p 2765 822 a(for) p 2910 822 a(a.e.) p Fn 3096 822 a(!) p Fo 3156 822 a(.) 448 1071 y @beginspecial @setspecial @endspecial(Pr) p 543 1071 a(o) p 584 1071 a(of.) p Fp 728 1071 a(By) p 871 1071 a(Sc) m(h) m(w) m(arz) p 1222 1071 a(inequalit) m(y) p 1607 1071 a(,) p 1661 1071 a(w) m(e) p 1795 1071 a(ha) m(v) m(e) p Fi 733 1165 a(Z) p Fl 779 1354 a(\012) p Fn 849 1280 a(d) p Fe(P) p Fh(j) p Fp(\() p Fn(Qx) p Fl 1151 1294 a(1) p Fn 1192 1280 a(P) p Fp 1263 1280 a(\)\() p Fn(!) p Fp 1408 1280 a(;) p Fn 1448 1280 a(x;) p 1540 1280 a(y) p Fp 1588 1280 a(\)) p Fh(j) p Fp 448 1280 a(\(3.17\)) 733 1502 y(=) p Fi 857 1421 a(X) p Fj 829 1620 a(z) p Fm 865 1620 a(2) p Fg(Z) p 928 1620 a(Z) p Ff 970 1594 a(d) p Fi 1022 1387 a(Z) p Fl 1068 1576 a(\012) p Fn 1138 1502 a(d) p Fe(P) p Fh(j) p Fn(Q) p Fp(\() p Fn(!) p Fp 1464 1502 a(;) p Fn 1504 1502 a(x;) p 1596 1502 a(z) p Fp 1642 1502 a(\)) p Fh(jj) p Fn(z) p Fl 1769 1516 a(1) p Fh 1811 1502 a(jj) p Fn(P) p Fp 1932 1502 a(\() p Fn(!) p Fp 2043 1502 a(;) p Fn 2083 1502 a(z) t(;) p 2169 1502 a(y) p Fp 2217 1502 a(\)) p Fh(j) 733 1787 y(\024) p Fi 857 1706 a(X) p Fj 829 1904 a(z) p Fm 865 1904 a(2) p Fg(Z) p 928 1904 a(Z) p Ff 970 1879 a(d) p Fi 1006 1693 a(\020) 1056 1672 y(Z) p Fl 1102 1860 a(\012) p Fn 1172 1787 a(d) p Fe(P) p Fh(j) p Fn(Q) p Fp(\() p Fn(!) p Fp 1499 1787 a(;) p Fn 1539 1787 a(x;) p 1631 1787 a(z) p Fp 1677 1787 a(\)) p Fh(j) p Fl 1737 1749 a(2) p Fh 1778 1787 a(j) p Fn(z) p Fl 1845 1801 a(1) p Fh 1885 1787 a(j) p Fi 1910 1693 a(\021) p Fl 1959 1716 a(1) p Fj(=) p Fl(2) p Fi 2069 1693 a(\020) 2119 1672 y(Z) p Fl 2165 1860 a(\012) p Fn 2235 1787 a(d) p Fe(P) p Fh(j) p Fn(P) p Fp 2449 1787 a(\() p Fn(!) p Fp 2561 1787 a(;) p Fn 2601 1787 a(z) t(;) p 2687 1787 a(y) p Fp 2735 1787 a(\)) p Fh(j) p Fl 2795 1749 a(2) p Fh 2836 1787 a(j) p Fn(z) p Fl 2903 1801 a(1) p Fh 2943 1787 a(j) p Fi 2968 1693 a(\021) p Fl 3018 1716 a(1) p Fj(=) p Fl(2) p Fn 3128 1787 a(:) 448 2062 y @beginspecial @setspecial @endspecial Fp(Since) p Fn 686 2062 a(P) p Fp 757 2062 a(,) p Fn 812 2062 a(Q) p Fh 909 2062 a(2) p 995 2062 a(D) p Fp 1068 2062 a(\() p Fn(@) p Fl 1151 2076 a(1) p Fp 1191 2062 a(\),) 1045 2255 y(RHS) p 1261 2255 a(of) p 1364 2255 a(\(3.17\)) p Fh 1045 2431 a(\024) p Fp 1151 2370 a(1) p 1151 2410 46 4 v 1151 2493 a(2) p Fi 1250 2350 a(X) p Fj 1221 2549 a(z) p Fm 1257 2549 a(2) p Fg(Z) p 1320 2549 a(Z) p Ff 1363 2523 a(d) p Fi 1414 2316 a(Z) p Fl 1461 2505 a(\012) p Fn 1531 2431 a(d) p Fe(P) p Fh(j) p Fn(Q) p Fp(\() p Fn(!) p Fp 1857 2431 a(;) p Fn 1897 2431 a(x;) p 1989 2431 a(z) p Fp 2035 2431 a(\)) p Fh(j) p Fl 2095 2393 a(2) p Fp 2136 2431 a(\() p Fh(j) p Fn(x) p Fl 2248 2445 a(1) p Fh 2308 2431 a(\000) p Fn 2399 2431 a(z) p Fl 2441 2445 a(1) p Fh 2481 2431 a(j) p Fp 2526 2431 a(+) p Fh 2617 2431 a(j) p Fn(x) p Fl 2694 2445 a(1) p Fh 2734 2431 a(j) p Fp(\)) 1136 2715 y(+) 1217 2653 y(1) p 1217 2693 V 1217 2777 a(2) p Fi 1316 2634 a(X) p Fj 1287 2832 a(z) p Fm 1323 2832 a(2) p Fg(Z) p 1386 2832 a(Z) p Ff 1429 2807 a(d) p Fi 1480 2600 a(Z) p Fl 1526 2788 a(\012) p Fn 1596 2715 a(d) p Fe(P) p Fh(j) p Fn(P) p Fp 1810 2715 a(\() p Fn(!) p Fp 1922 2715 a(;) p Fn 1962 2715 a(z) t(;) p 2048 2715 a(y) p Fp 2096 2715 a(\)) p Fh(j) p Fl 2156 2677 a(2) p Fp 2197 2715 a(\() p Fh(j) p Fn(z) p Fl 2299 2729 a(1) p Fh 2359 2715 a(\000) p Fn 2450 2715 a(y) p Fl 2495 2729 a(1) p Fh 2534 2715 a(j) p Fp 2580 2715 a(+) p Fh 2671 2715 a(j) p Fn(y) p Fl 2741 2729 a(1) p Fh 2780 2715 a(j) p Fp(\)) p Fh 1045 2975 a(\024) p Fn 1141 2975 a(C) p Fi 1213 2881 a(\020) p Fh 1262 2975 a(k) p Fn(@) p Fl 1355 2989 a(1) p Fn 1395 2975 a(Q) p Fh(k) p Fl 1512 2938 a(2) p Fm 1512 3002 a(L) p Fc 1561 2983 a(2) p Fp 1620 2975 a(+) p Fh 1711 2975 a(j) p Fn(x) p Fl 1788 2989 a(1) p Fh 1827 2975 a(jk) p Fn(Q) p Fh(k) p Fl 2014 2938 a(2) p Fm 2014 3002 a(L) p Fc 2063 2983 a(2) p Fp 1045 3158 a(+) p Fh(k) p Fn(@) p Fl 1209 3172 a(1) p Fn 1249 3158 a(P) p Fh 1320 3158 a(k) p Fl 1365 3121 a(2) p Fm 1365 3185 a(L) p Fc 1414 3166 a(2) p Fp 1473 3158 a(+) p Fh 1564 3158 a(j) p Fn(y) p Fl 1634 3172 a(1) p Fh 1673 3158 a(jk) p Fn(P) p Fh 1814 3158 a(k) p Fl 1859 3121 a(2) p Fm 1859 3185 a(L) p Fc 1908 3166 a(2) p Fi 1947 3064 a(\021) p Fh 1045 3307 a(\024) p Fn 1141 3307 a(C) p Fj 1206 3321 a(x;y) p Fn 1332 3307 a(<) p Fh 1428 3307 a(1) p Fn(;) 448 3501 y @beginspecial @setspecial @endspecial Fp(for) p 587 3501 a(some) p 815 3501 a(constan) m(ts) p Fn 1218 3501 a(C) p Fp 1290 3501 a(,) p Fn 1345 3501 a(C) p Fj 1410 3515 a(x;y) p Fp 1541 3501 a(dep) s(ending) p 1978 3501 a(on) p Fn 2104 3501 a(x) p Fp(,) p Fn 2211 3501 a(y) p Fh 2285 3501 a(2) p Fk 2370 3501 a(Z) p 2390 3501 a(Z) p Fj 2445 3464 a(d) p Fp 2486 3501 a(.) p 2551 3436 60 4 v 2551 3525 4 89 v 2607 3525 V 2551 3528 60 4 v Fe 448 3750 a(Lemma) p 819 3750 a(3.8) p 998 3750 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1094 3750 a(P) p Fh 1190 3750 a(2) p 1276 3750 a(D) p Fp 1349 3750 a(\() p Fn(@) p Fl 1432 3764 a(1) p Fp 1471 3750 a(\)) p Fo(,) p 1567 3750 a(we) p 1702 3750 a(have) p Fh 1400 3943 a(L) p Fj 1463 3957 a(H) p Ff 1521 3965 a(!) p Fp 1570 3943 a(\() p Fn(Qx) p Fl 1729 3957 a(1) p Fn 1768 3943 a(P) p Fp 1839 3943 a(\)) p 1900 3943 a(=) p Fn 1996 3943 a(Q) p Fh(L) p Fj 2131 3957 a(H) p Ff 2189 3965 a(!) p Fp 2237 3943 a(\() p Fn(x) p Fl 2324 3957 a(1) p Fp 2364 3943 a(\)) p Fn(P) s(:) 448 4136 y @beginspecial @setspecial @endspecial Fo(In) p 567 4136 a(p) p 608 4136 a(articular,) p Fh 1011 4136 a(L) p Fj 1074 4150 a(H) p Ff 1132 4158 a(!) p Fp 1180 4136 a(\() p Fn(Qx) p Fl 1339 4150 a(1) p Fn 1379 4136 a(P) p Fp 1450 4136 a(\)) p Fh 1511 4136 a(2) p 1596 4136 a(L) p Fl 1659 4103 a(2) p Fo 1699 4136 a(.) 448 4385 y @beginspecial @setspecial @endspecial(Pr) p 543 4385 a(o) p 584 4385 a(of.) p Fp 726 4385 a(By) p 864 4385 a(Lemma) p 1183 4385 a(3.7,) p 1351 4385 a(\() p Fn(Qx) p Fl 1510 4399 a(1) p Fn 1549 4385 a(P) p Fp 1620 4385 a(\)\() p Fn(!) p Fp 1766 4385 a(;) p Fn 1806 4385 a(x;) p 1898 4385 a(y) p Fp 1946 4385 a(\)) p 2007 4385 a(is) p 2093 4385 a(\014nite) p 2320 4385 a(for) p 2454 4385 a(a.e.) p Fn 2629 4385 a(!) p Fp 2689 4385 a(.) p 2753 4385 a(Th) m(us,) p 3004 4385 a(b) m(y) p 3125 4385 a(Remark) 448 4509 y(3.3,) p Fh 621 4509 a(L) p Fj 684 4523 a(H) p Ff 742 4531 a(!) p Fp 791 4509 a(\() p Fn(Qx) p Fl 950 4523 a(1) p Fn 990 4509 a(P) p Fp 1061 4509 a(\)) p 1127 4509 a(mak) m(es) p 1402 4509 a(sense) p 1636 4509 a(as) p 1749 4509 a(a) p 1825 4509 a(function) p 2182 4509 a(on) p 2310 4509 a(\012) p Fh 2396 4509 a(\002) p Fk 2488 4509 a(Z) p 2508 4509 a(Z) p Fj 2563 4472 a(d) p Fh 2624 4509 a(\002) p Fk 2716 4509 a(Z) p 2736 4509 a(Z) p Fj 2790 4472 a(d) p Fp 2862 4509 a(for) p 3002 4509 a(a.e.) p Fn 3182 4509 a(!) p Fp 3242 4509 a(.) p 3311 4509 a(W) p 3396 4509 a(e) 448 4634 y(will) p 620 4634 a(sho) m(w) p Fh 836 4827 a(L) p Fj 899 4841 a(V) p Ff 940 4849 a(!) p Fp 989 4827 a(\() p Fn(Qx) p Fl 1148 4841 a(1) p Fn 1188 4827 a(P) p Fp 1259 4827 a(\)) p 1319 4827 a(=) p Fh 1415 4827 a(L) p Fj 1478 4841 a(V) p Ff 1519 4849 a(!) p Fp 1568 4827 a(\() p Fn(Q) p Fp(\)) p Fn(x) p Fl 1762 4841 a(1) p Fn 1802 4827 a(P) p Fp 1893 4827 a(+) p Fn 1984 4827 a(Qx) p Fl 2108 4841 a(1) p Fh 2147 4827 a(L) p Fj 2210 4841 a(V) p Ff 2251 4849 a(!) p Fp 2300 4827 a(\() p Fn(P) p Fp 2406 4827 a(\)) p Fn(;) p Fp 448 4827 a(\(3.18\)) p Fh 830 4976 a(L) p Fj 893 4990 a(H) p Fc 951 4999 a(0) p Fp 989 4976 a(\() p Fn(Qx) p Fl 1148 4990 a(1) p Fn 1188 4976 a(P) p Fp 1259 4976 a(\)) p 1319 4976 a(=) p Fh 1415 4976 a(L) p Fj 1478 4990 a(H) p Fc 1536 4999 a(0) p Fp 1575 4976 a(\() p Fn(Q) p Fp(\)) p Fn(x) p Fl 1769 4990 a(1) p Fn 1809 4976 a(P) p Fp 1900 4976 a(+) p Fn 1991 4976 a(Q) p Fh(L) p Fj 2126 4990 a(H) p Fc 2184 4999 a(0) p Fp 2222 4976 a(\() p Fn(x) p Fl 2309 4990 a(1) p Fp 2349 4976 a(\)) p Fn(P) p Fp 2475 4976 a(+) p Fn 2566 4976 a(Qx) p Fl 2690 4990 a(1) p Fh 2729 4976 a(L) p Fj 2792 4990 a(H) p Fc 2850 4999 a(0) p Fp 2889 4976 a(\() p Fn(P) p Fp 2995 4976 a(\)) p Fn(;) p Fp 448 4976 a(\(3.19\)) 1897 5225 y(32) p eop %%Page: 33 33 33 32 bop 448 573 a @beginspecial @setspecial @endspecial Fp(as) p 558 573 a(functions) p 949 573 a(on) p 1073 573 a(\012) p Fh 1156 573 a(\002) p Fk 1243 573 a(Z) p 1263 573 a(Z) p Fj 1318 536 a(d) p Fh 1375 573 a(\002) p Fk 1463 573 a(Z) p 1483 573 a(Z) p Fj 1538 536 a(d) p Fp 1578 573 a(.) p 1643 573 a(Then,) p 1905 573 a(Lemma) p 2227 573 a(3.8) p 2372 573 a(follo) m(ws) p 2669 573 a(b) m(y) p 2794 573 a(using) p Fh 3030 573 a(L) p Fj 3093 587 a(H) p Ff 3151 595 a(!) p Fp 3199 573 a(\() p Fn(P) p Fp 3305 573 a(\)) p 3366 573 a(=) p Fh 448 697 a(L) p Fj 511 711 a(H) p Ff 569 719 a(!) p Fp 618 697 a(\() p Fn(Q) p Fp(\)) p 786 697 a(=) p 882 697 a(0.) p 993 697 a(T) p 1051 697 a(o) p 1127 697 a(pro) m(v) m(e) p 1372 697 a(\(3.18\),) p 1660 697 a(w) m(e) p 1794 697 a(compute) 1263 901 y(\() p Fh(L) p Fj 1361 915 a(V) p Ff 1402 923 a(!) p Fp 1451 901 a(\() p Fn(Qx) p Fl 1610 915 a(1) p Fn 1650 901 a(P) p Fp 1721 901 a(\)\)\() p Fn(!) p Fp 1902 901 a(;) p Fn 1942 901 a(x;) p 2034 901 a(y) p Fp 2082 901 a(\)) p 2143 901 a(=) p Fn 2239 901 a(I) p 2286 901 a(I) p 2333 901 a(I) p Fp 2401 901 a(+) p Fn 2492 901 a(I) p 2539 901 a(V) p 2597 901 a(;) 448 1104 y @beginspecial @setspecial @endspecial Fp(where) p Fn 918 1308 a(I) p 965 1308 a(I) p 1012 1308 a(I) p Fp 1084 1308 a(:=) p Fi 1235 1227 a(X) p Fj 1206 1426 a(z) p Fm 1242 1426 a(2) p Fg(Z) p 1305 1426 a(Z) p Ff 1347 1400 a(d) p Fn 1399 1308 a(Q) p Fp(\() p Fn(!) p Fp 1581 1308 a(;) p Fn 1621 1308 a(x;) p 1713 1308 a(z) p Fp 1759 1308 a(\)) p Fn 1809 1308 a(z) p Fl 1851 1322 a(1) p Fn 1907 1308 a(P) p Fp 1978 1308 a(\() p Fn(!) p Fp 2089 1308 a(;) p Fn 2129 1308 a(z) t(;) p 2215 1308 a(y) p Fp 2263 1308 a(\)\() p Fn(V) p Fj 2386 1322 a(!) p Fp 2438 1308 a(\() p Fn(x) p Fp(\)) p Fh 2580 1308 a(\000) p Fn 2671 1308 a(V) p Fj 2724 1322 a(!) p Fp 2775 1308 a(\() p Fn(z) p Fp 2856 1308 a(\)\)) p Fn(;) 958 1560 y(I) p 1005 1560 a(V) p Fp 1104 1560 a(:=) p Fi 1254 1480 a(X) p Fj 1225 1678 a(z) p Fm 1261 1678 a(2) p Fg(Z) p 1324 1678 a(Z) p Ff 1367 1653 a(d) p Fn 1418 1560 a(Q) p Fp(\() p Fn(!) p Fp 1600 1560 a(;) p Fn 1640 1560 a(x;) p 1732 1560 a(z) p Fp 1778 1560 a(\)) p Fn 1828 1560 a(z) p Fl 1870 1574 a(1) p Fn 1926 1560 a(P) p Fp 1997 1560 a(\() p Fn(!) p Fp 2108 1560 a(;) p Fn 2148 1560 a(z) t(;) p 2234 1560 a(y) p Fp 2282 1560 a(\)\() p Fn(V) p Fj 2405 1574 a(!) p Fp 2457 1560 a(\() p Fn(z) p Fp 2538 1560 a(\)) p Fh 2594 1560 a(\000) p Fn 2685 1560 a(V) p Fj 2738 1574 a(!) p Fp 2788 1560 a(\() p Fn(y) p Fp 2871 1560 a(\)\)) p Fn(:) 448 1841 y @beginspecial @setspecial @endspecial Fp(W) p 533 1841 a(e) p 615 1841 a(will) p 797 1841 a(sho) m(w) p 1032 1841 a(that,) p Fn 1267 1841 a(I) p 1314 1841 a(I) p 1361 1841 a(I) p Fp 1408 1841 a(,) p Fn 1476 1841 a(I) p 1523 1841 a(V) p Fp 1637 1841 a(mak) m(e) p 1884 1841 a(sense) p 2128 1841 a(for) p 2277 1841 a(a.e.) p Fn 2484 1841 a(!) p Fp 2544 1841 a(.) p 2639 1841 a(In) p 2763 1841 a(fact,) p 2980 1841 a(b) m(y) p 3116 1841 a(Sc) m(h) m(w) m(arz) 448 1966 y(inequalit) m(y) p 833 1966 a(,) p Fi 732 2076 a(Z) p Fl 779 2265 a(\012) p Fn 849 2191 a(d) p Fe(P) p Fh(j) p Fn(I) p 1039 2191 a(I) p 1086 2191 a(I) p Fh 1133 2191 a(j) q(\024) p Fi 1255 2097 a(\020) 1305 2076 y(Z) p Fl 1351 2265 a(\012) p Fn 1421 2191 a(d) p Fe(P) p Fi 1584 2111 a(X) p Fj 1555 2309 a(z) p Fm 1591 2309 a(2) p Fg(Z) p 1654 2309 a(Z) p Ff 1697 2284 a(d) p Fh 1748 2191 a(j) p Fn(Q) p Fp(\() p Fn(!) p Fp 1956 2191 a(;) p Fn 1996 2191 a(x;) p 2088 2191 a(z) p Fp 2134 2191 a(\)) p Fh(j) p Fl 2194 2154 a(2) p Fh 2235 2191 a(j) p Fn(V) p Fj 2313 2205 a(!) p Fp 2363 2191 a(\() p Fn(x) p Fp(\)) p Fh 2506 2191 a(\000) p Fn 2597 2191 a(V) p Fj 2650 2205 a(!) p Fp 2701 2191 a(\() p Fn(z) p Fp 2782 2191 a(\)) p Fh(j) p Fl 2842 2154 a(2) p Fi 2882 2097 a(\021) p Fl 2932 2120 a(1) p Fj(=) p Fl(2) p Fh 3062 2191 a(\002) 1250 2476 y(\002) p Fi 1321 2382 a(\020) 1371 2361 y(Z) p Fl 1417 2550 a(\012) p Fn 1487 2476 a(d) p Fe(P) p Fi 1650 2395 a(X) p Fj 1621 2594 a(z) p Fm 1657 2594 a(2) p Fg(Z) p 1720 2594 a(Z) p Ff 1763 2568 a(d) p Fh 1814 2476 a(j) p Fn(z) p Fl 1881 2490 a(1) p Fh 1921 2476 a(j) p Fl 1946 2438 a(2) p Fh 1986 2476 a(j) p Fn(P) p Fp 2082 2476 a(\() p Fn(!) p Fp 2192 2476 a(;) p Fn 2232 2476 a(z) t(;) p 2318 2476 a(y) p Fp 2366 2476 a(\)) p Fh(j) p Fl 2426 2438 a(2) p Fi 2467 2382 a(\021) p Fl 2517 2405 a(1) p Fj(=) p Fl(2) p Fn 2627 2476 a(:) 448 2762 y @beginspecial @setspecial @endspecial Fp(Since) p Fn 686 2762 a(P) p Fp 787 2762 a(satis\014es) p 1122 2762 a(Assumption) p 1625 2762 a(\(1.6\),) p Fi 1109 2871 a(Z) p Fl 1155 3060 a(\012) p Fn 1225 2986 a(d) p Fe(P) p Fi 1373 2906 a(X) p Fj 1344 3104 a(z) p Fm 1380 3104 a(2) p Fg(Z) p 1443 3104 a(Z) p Ff 1485 3079 a(d) p Fh 1537 2986 a(j) p Fn(z) p Fl 1604 3000 a(1) p Fh 1644 2986 a(j) p Fl 1669 2949 a(2) p Fh 1708 2986 a(j) p Fn(P) p Fp 1804 2986 a(\() p Fn(!) p Fp 1915 2986 a(;) p Fn 1955 2986 a(z) t(;) p 2041 2986 a(y) p Fp 2089 2986 a(\)) p Fh(j) p Fl 2149 2949 a(2) p Fh 1344 3265 a(\024) p Fp 1440 3265 a(2) p Fi 1500 3150 a(Z) p Fl 1546 3339 a(\012) p Fn 1617 3265 a(d) p Fe(P) p Fi 1780 3184 a(X) p Fj 1751 3383 a(z) p Fm 1787 3383 a(2) p Fg(Z) p 1850 3383 a(Z) p Ff 1892 3357 a(d) p Fh 1944 3265 a(j) p Fn(z) p Fl 2011 3279 a(1) p Fh 2071 3265 a(\000) p Fn 2162 3265 a(y) p Fl 2207 3279 a(1) p Fh 2246 3265 a(j) p Fl 2271 3227 a(2) p Fh 2310 3265 a(j) p Fn(P) p Fp 2406 3265 a(\() p Fn(!) p Fp 2517 3265 a(;) p Fn 2557 3265 a(z) t(;) p 2643 3265 a(y) p Fp 2691 3265 a(\)) p Fh(j) p Fl 2751 3227 a(2) p Fp 1435 3543 a(+2) p Fh(j) p Fn(y) p Fl 1621 3557 a(1) p Fh 1660 3543 a(j) p Fl 1685 3506 a(2) p Fi 1740 3428 a(Z) p Fl 1786 3617 a(\012) p Fn 1856 3543 a(d) p Fe(P) p Fi 2019 3462 a(X) p Fj 1990 3661 a(z) p Fm 2026 3661 a(2) p Fg(Z) p 2089 3661 a(Z) p Ff 2132 3635 a(d) p Fh 2183 3543 a(j) p Fn(P) p Fp 2279 3543 a(\() p Fn(!) p Fp 2390 3543 a(;) p Fn 2430 3543 a(z) t(;) p 2516 3543 a(y) p Fp 2564 3543 a(\)) p Fh(j) p Fl 2624 3506 a(2) p Fh 1344 3769 a(\024) p Fn 1440 3769 a(C) p Fj 1505 3783 a(y) p Fn 1571 3769 a(<) p Fh 1667 3769 a(1) p Fn(;) 448 3972 y @beginspecial @setspecial @endspecial Fp(for) p 587 3972 a(some) p 815 3972 a(constan) m(t) p Fn 1182 3972 a(C) p Fj 1247 3986 a(y) p Fp 1319 3972 a(dep) s(ending) p 1755 3972 a(only) p 1955 3972 a(on) p Fn 2081 3972 a(y) p Fh 2154 3972 a(2) p Fk 2240 3972 a(Z) p 2260 3972 a(Z) p Fj 2315 3935 a(d) p Fp 2355 3972 a(.) p 2421 3972 a(Since) p Fn 2658 3972 a(Q) p Fh 2756 3972 a(2) p 2841 3972 a(D) p Fp 2914 3972 a(\() p Fh(L) p Fj 3012 3986 a(H) p Ff 3070 3994 a(!) p Fp 3119 3972 a(\),) p Fi 1169 4086 a(Z) p Fl 1215 4275 a(\012) p Fn 1286 4201 a(d) p Fe(P) p Fi 1433 4120 a(X) p Fj 1404 4319 a(z) p Fm 1440 4319 a(2) p Fg(Z) p 1503 4319 a(Z) p Ff 1546 4293 a(d) p Fh 1597 4201 a(j) p Fn(Q) p Fp(\() p Fn(!) p Fp 1805 4201 a(;) p Fn 1845 4201 a(x;) p 1937 4201 a(z) p Fp 1983 4201 a(\)) p Fh(j) p Fl 2043 4164 a(2) p Fh 2084 4201 a(j) p Fn(V) p Fj 2162 4215 a(!) p Fp 2213 4201 a(\() p Fn(x) p Fp(\)) p Fh 2355 4201 a(\000) p Fn 2446 4201 a(V) p Fj 2499 4215 a(!) p Fp 2550 4201 a(\() p Fn(z) p Fp 2631 4201 a(\)) p Fh(j) p Fl 2691 4164 a(2) p Fp 1244 4445 a(=) p Fh 1404 4445 a(kL) p Fj 1512 4459 a(V) p Ff 1553 4467 a(!) p Fp 1603 4445 a(\() p Fn(Q) p Fp(\)) p Fh(k) p Fl 1790 4407 a(2) p Fm 1790 4472 a(L) p Fc 1839 4453 a(2) p Fn 1903 4445 a(<) p Fh 1999 4445 a(1) p Fn(:) 448 4648 y @beginspecial @setspecial @endspecial Fp(Therefore,) p Fn 879 4648 a(I) p 926 4648 a(I) p 973 4648 a(I) p Fp 1041 4648 a(mak) m(es) p 1306 4648 a(sense) p 1530 4648 a(for) p 1660 4648 a(a.e.) p Fn 1834 4648 a(!) p Fp 1894 4648 a(,) p 1943 4648 a(and) p 2111 4648 a(so) p 2213 4648 a(do) s(es) p Fn 2410 4648 a(I) p 2457 4648 a(V) p Fp 2551 4648 a(b) m(y) p 2669 4648 a(the) p 2816 4648 a(same) p 3035 4648 a(argumen) m(t.) 448 4773 y(Since) p Fn 773 4976 a(I) p 820 4976 a(I) p 867 4976 a(I) p Fp 934 4976 a(+) p Fn 1025 4976 a(I) p 1072 4976 a(V) p Fp 1171 4976 a(=) p 1267 4976 a(\() p Fh(L) p Fj 1365 4990 a(V) p Ff 1406 4998 a(!) p Fp 1455 4976 a(\() p Fn(Q) p Fp(\)) p Fn(x) p Fl 1649 4990 a(1) p Fn 1689 4976 a(P) p Fp 1760 4976 a(\)\() p Fn(!) p Fp 1906 4976 a(;) p Fn 1946 4976 a(x;) p 2038 4976 a(y) p Fp 2086 4976 a(\)) p 2142 4976 a(+) p 2233 4976 a(\() p Fn(Qx) p Fl 2392 4990 a(1) p Fh 2431 4976 a(L) p Fj 2494 4990 a(V) p Ff 2535 4998 a(!) p Fp 2584 4976 a(\() p Fn(P) p Fp 2690 4976 a(\)\)\() p Fn(!) p Fp 2871 4976 a(;) p Fn 2911 4976 a(x;) p 3003 4976 a(y) p Fp 3051 4976 a(\)) p Fn(;) p Fp 1897 5225 a(33) p eop %%Page: 34 34 34 33 bop 448 573 a @beginspecial @setspecial @endspecial Fp(w) m(e) p 582 573 a(pro) m(v) m(ed) p 878 573 a(\(3.18\).) 589 697 y @beginspecial @setspecial @endspecial(T) p 647 697 a(o) p 738 697 a(pro) m(v) m(e) p 998 697 a(\(3.19\),) p 1305 697 a(w) m(e) p 1453 697 a(notice) p 1736 697 a(that,) p 1977 697 a(b) m(y) p 2118 697 a(Remark) p 2475 697 a(3.3,) p 2666 697 a(\() p Fn(H) p Fl 2777 711 a(0) p Fn 2816 697 a(Qx) p Fl 2940 711 a(1) p Fn 2979 697 a(P) p Fp 3050 697 a(\)\() p Fn(!) p Fp 3196 697 a(;) p Fn 3236 697 a(x;) p 3328 697 a(y) p Fp 3376 697 a(\),) 448 822 y(\() p Fn(QH) p Fl 631 836 a(0) p Fn 671 822 a(x) p Fl 723 836 a(1) p Fn 762 822 a(P) p Fp 833 822 a(\)\() p Fn(!) p Fp 979 822 a(;) p Fn 1019 822 a(x;) p 1111 822 a(y) p Fp 1159 822 a(\),) p 1243 822 a(\() p Fn(Qx) p Fl 1402 836 a(1) p Fn 1442 822 a(H) p Fl 1518 836 a(0) p Fn 1557 822 a(P) p Fp 1628 822 a(\)\() p Fn(!) p Fp 1774 822 a(;) p Fn 1814 822 a(x;) p 1906 822 a(y) p Fp 1954 822 a(\),) p 2038 822 a(and) p 2206 822 a(\() p Fn(Qx) p Fl 2365 836 a(1) p Fn 2405 822 a(P) p 2476 822 a(H) p Fl 2552 836 a(0) p Fp 2591 822 a(\)\() p Fn(!) p Fp 2737 822 a(;) p Fn 2777 822 a(x;) p 2869 822 a(y) p Fp 2917 822 a(\)) p 2974 822 a(are) p 3117 822 a(all) p 3235 822 a(\014nite) 448 946 y(for) p 587 946 a(a.e.) p Fn 764 946 a(!) p Fp 824 946 a(.) p 890 946 a(Then,) 776 1139 y(\() p Fh(L) p Fj 874 1153 a(H) p Fc 932 1162 a(0) p Fp 971 1139 a(\() p Fn(Qx) p Fl 1130 1153 a(1) p Fn 1169 1139 a(P) p Fp 1240 1139 a(\)) q(\)\() p Fn(!) p Fp 1421 1139 a(;) p Fn 1461 1139 a(x;) p 1553 1139 a(y) p Fp 1601 1139 a(\)) 1088 1288 y(=) p 1276 1288 a(\() p Fn(H) p Fl 1387 1302 a(0) p Fn 1426 1288 a(Qx) p Fl 1550 1302 a(1) p Fn 1589 1288 a(P) p Fp 1660 1288 a(\)\() p Fn(!) p Fp 1806 1288 a(;) p Fn 1846 1288 a(x;) p 1938 1288 a(y) p Fp 1986 1288 a(\)) p Fh 2042 1288 a(\000) p Fp 2133 1288 a(\() p Fn(Qx) p Fl 2292 1302 a(1) p Fn 2332 1288 a(P) p 2403 1288 a(H) p Fl 2479 1302 a(0) p Fp 2518 1288 a(\)\() p Fn(!) p Fp 2663 1288 a(;) p Fn 2703 1288 a(x;) p 2795 1288 a(y) p Fp 2843 1288 a(\)) 1088 1437 y(=) p 1276 1437 a(\() p Fn(H) p Fl 1387 1451 a(0) p Fn 1426 1437 a(Qx) p Fl 1550 1451 a(1) p Fn 1589 1437 a(P) p Fp 1660 1437 a(\)\() p Fn(!) p Fp 1806 1437 a(;) p Fn 1846 1437 a(x;) p 1938 1437 a(y) p Fp 1986 1437 a(\)) p Fh 2042 1437 a(\000) p Fp 2133 1437 a(\() p Fn(QH) p Fl 2316 1451 a(0) p Fn 2355 1437 a(x) p Fl 2407 1451 a(1) p Fn 2447 1437 a(P) p Fp 2518 1437 a(\)\() p Fn(!) p Fp 2663 1437 a(;) p Fn 2703 1437 a(x;) p 2795 1437 a(y) p Fp 2843 1437 a(\)) 1276 1587 y(+\() p Fn(QH) p Fl 1530 1601 a(0) p Fn 1569 1587 a(x) p Fl 1621 1601 a(1) p Fn 1660 1587 a(P) p Fp 1731 1587 a(\)\() p Fn(!) p Fp 1877 1587 a(;) p Fn 1917 1587 a(x;) p 2009 1587 a(y) p Fp 2057 1587 a(\)) p Fh 2113 1587 a(\000) p Fp 2204 1587 a(\() p Fn(Qx) p Fl 2363 1601 a(1) p Fn 2402 1587 a(H) p Fl 2478 1601 a(0) p Fn 2517 1587 a(P) p Fp 2588 1587 a(\)\() p Fn(!) p Fp 2734 1587 a(;) p Fn 2774 1587 a(x;) p 2866 1587 a(y) p Fp 2914 1587 a(\)) 1276 1736 y(+\() p Fn(Qx) p Fl 1506 1750 a(1) p Fn 1545 1736 a(H) p Fl 1621 1750 a(0) p Fn 1660 1736 a(P) p Fp 1731 1736 a(\)\() p Fn(!) p Fp 1877 1736 a(;) p Fn 1917 1736 a(x;) p 2009 1736 a(y) p Fp 2057 1736 a(\)) p Fh 2113 1736 a(\000) p Fp 2204 1736 a(\() p Fn(Qx) p Fl 2363 1750 a(1) p Fn 2402 1736 a(P) p 2473 1736 a(H) p Fl 2549 1750 a(0) p Fp 2588 1736 a(\)\() p Fn(!) p Fp 2734 1736 a(;) p Fn 2774 1736 a(x;) p 2866 1736 a(y) p Fp 2914 1736 a(\)) 1088 1886 y(=) p 1276 1886 a(\() p Fh(L) p Fj 1374 1900 a(H) p Fc 1432 1909 a(0) p Fp 1470 1886 a(\() p Fn(Q) p Fp(\)) p Fn(x) p Fl 1664 1900 a(1) p Fn 1704 1886 a(P) p Fp 1775 1886 a(\)\() p Fn(!) p Fp 1921 1886 a(;) p Fn 1961 1886 a(x;) p 2053 1886 a(y) p Fp 2101 1886 a(\)) p 2157 1886 a(+) p 2248 1886 a(\() p Fn(Q) p Fh(L) p Fj 2418 1900 a(H) p Fc 2476 1909 a(0) p Fp 2515 1886 a(\() p Fn(x) p Fl 2602 1900 a(1) p Fp 2642 1886 a(\)) p Fn(P) p Fp 2748 1886 a(\)\() p Fn(!) p Fp 2894 1886 a(;) p Fn 2934 1886 a(x;) p 3026 1886 a(y) p Fp 3074 1886 a(\)) 1276 2035 y(+\() p Fn(Qx) p Fl 1506 2049 a(1) p Fh 1545 2035 a(L) p Fj 1608 2049 a(H) p Fc 1666 2058 a(0) p Fp 1704 2035 a(\() p Fn(P) p Fp 1810 2035 a(\)\)\() p Fn(!) p Fp 1992 2035 a(;) p Fn 2032 2035 a(x;) p 2124 2035 a(y) p Fp 2172 2035 a(\)) p Fn(:) 448 2227 y @beginspecial @setspecial @endspecial Fp(Th) m(us) p 679 2227 a(\(3.19\)) p 941 2227 a(is) p 1033 2227 a(pro) m(v) m(ed.) p 1364 2163 60 4 v 1364 2252 4 89 v 1419 2252 V 1364 2255 60 4 v 448 2476 a @beginspecial @setspecial @endspecial(The) p 635 2476 a(follo) m(wing) p 1019 2476 a(lemma) p 1312 2476 a(follo) m(ws) p 1610 2476 a(b) m(y) p 1737 2476 a(simple) p 2020 2476 a(argumen) m(t) p 2427 2476 a(of) p 2530 2476 a(functional) p 2957 2476 a(calculus.) p Fe 448 2611 a(Lemma) p 819 2611 a(3.9) p 998 2611 a @beginspecial @setspecial @endspecial Fp 852 2803 a(lim) p Fj 863 2863 a(\016) p Fm 896 2863 a(#) p Fl(0) p Fp 979 2803 a(\() p Fh(\000) p Fn(i\016) p Fh 1180 2803 a(\000) p 1271 2803 a(L) p Fj 1334 2817 a(H) p Ff 1392 2825 a(!) p Fp 1441 2803 a(\)) p Fm 1476 2766 a(\000) p Fl(1) p Fh 1570 2803 a(L) p Fj 1633 2817 a(H) p Ff 1691 2825 a(!) p Fn 1740 2803 a(A) p Fp 1833 2803 a(=) p Fh 1929 2803 a(\000) p Fn(A;) p Fo 2201 2803 a(for) p Fn 2347 2803 a(A) p Fh 2440 2803 a(2) p Fp 2526 2803 a(\() p Fo(Ker) p Fh 2744 2803 a(L) p Fj 2807 2817 a(H) p Ff 2865 2825 a(!) p Fp 2913 2803 a(\)) p Fm 2948 2766 a(?) p Fn 3008 2803 a(:) p Fe 448 3134 a(Lemma) p 819 3134 a(3.10) p 1050 3134 a @beginspecial @setspecial @endspecial Fi 1412 3232 a(h) p Fp 1451 3326 a([) p Fn(x) p Fl 1528 3340 a(1) p Fn 1568 3326 a(;) p 1608 3326 a(P) p Fp 1679 3326 a(]) p Fn(;) p 1744 3326 a(P) p Fi 1815 3232 a(i) p Fh 1880 3326 a(2) p Fp 1966 3326 a(\() p Fo(Ker) p Fh 2184 3326 a(L) p Fj 2247 3340 a(H) p Ff 2305 3348 a(!) p Fp 2354 3326 a(\)) p Fm 2389 3288 a(?) p Fn 2448 3326 a(:) 448 3767 y @beginspecial @setspecial @endspecial Fo(Pr) p 543 3767 a(o) p 584 3767 a(of.) p Fp 728 3767 a(By) p 871 3767 a(Prop) s(osition) p 1360 3767 a(2.5,) p Fn 1065 3959 a(<) p 1161 3959 a(A;) p Fi 1269 3865 a(h) p Fp 1309 3959 a([) p Fn(x) p Fl 1386 3973 a(1) p Fn 1426 3959 a(;) p 1466 3959 a(P) p Fp 1537 3959 a(]) p Fn(;) p 1602 3959 a(P) p Fi 1673 3865 a(i) p Fn 1738 3959 a(>) p Fm 1809 3979 a(L) p Fc 1858 3960 a(2) p Fp 1896 3959 a(=) p Fn(<) p Fp 2063 3959 a([) p Fn(A;) p 2196 3959 a(P) p Fp 2267 3959 a(]) p Fn(;) p Fp 2332 3959 a([) p Fn(x) p Fl 2409 3973 a(1) p Fn 2450 3959 a(;) p 2490 3959 a(P) p Fp 2561 3959 a(]) p Fn 2612 3959 a(>) p Fm 2683 3979 a(L) p Fc 2732 3960 a(2) p Fn 2795 3959 a(:) 448 4151 y @beginspecial @setspecial @endspecial Fp(Th) m(us,) p 704 4151 a(it) p 795 4151 a(su\016ces) p 1104 4151 a(to) p 1215 4151 a(sho) m(w) 1361 4343 y([) p Fn(A;) p 1494 4343 a(P) p Fp 1565 4343 a(]) p 1617 4343 a(=) p 1713 4343 a(0) p Fn(;) p Fp 1889 4343 a(if) p Fn 1973 4343 a(A) p Fh 2066 4343 a(2) p Fp 2152 4343 a(Ker) p Fh 2329 4343 a(L) p Fj 2392 4357 a(H) p Ff 2450 4365 a(!) p Fn 2499 4343 a(:) p Fp 448 4343 a(\(3.20\)) 448 4535 y @beginspecial @setspecial @endspecial(Let) p Fn 619 4535 a(A) p Fj 687 4549 a(n) p Fh 772 4535 a(2) p 871 4535 a(A) p Fl 944 4549 a(0) p Fp 1021 4535 a(so) p 1140 4535 a(that) p Fn 1345 4535 a(A) p Fj 1413 4549 a(n) p Fh 1498 4535 a(!) p Fn 1627 4535 a(A) p Fp 1733 4535 a(in) p Fh 1847 4535 a(L) p Fl 1910 4502 a(2) p Fp 1987 4535 a(as) p Fn 2107 4535 a(n) p Fh 2199 4535 a(!) p 2328 4535 a(1) p Fp 2457 4535 a(\(Prop) s(osition) p 2990 4535 a(2.3\).) p 3230 4535 a(Since) p Fn 448 4660 a(A) p Fj 516 4674 a(n) p Fh 589 4660 a(2) p 675 4660 a(A) p Fl 748 4674 a(0) p Fp 787 4660 a(,) p 842 4660 a(\() p Fn(z) p Fh 944 4660 a(\000) p Fn 1034 4660 a(H) p Fj 1110 4674 a(!) p Fp 1160 4660 a(\)) p Fm 1195 4627 a(\000) p Fl(1) p Fp 1290 4660 a(\() p Fn(z) p Fh 1392 4660 a(\000) p Fn 1482 4660 a(H) p Fj 1558 4674 a(!) p Fp 1608 4660 a(\)) p Fn(A) p Fj 1711 4674 a(n) p Fp 1784 4660 a(=) p Fn 1880 4660 a(A) p Fj 1948 4674 a(n) p Fp 2025 4660 a(\(Im) p Fn 2199 4660 a(z) p Fh 2271 4660 a(6) p Fp(=) p 2367 4660 a(0\)) p 2478 4660 a(mak) m(es) p 2751 4660 a(sense) p 2984 4660 a(as) p 3096 4660 a(elemen) m(ts) 448 4784 y(of) p Fh 552 4784 a(L) p Fl 615 4751 a(2) p Fp 654 4784 a(.) p 720 4784 a(Then,) 928 4976 y([) p Fn(A) p Fj 1021 4990 a(n) p Fn 1068 4976 a(;) p Fp 1108 4976 a(\() p Fn(z) p Fh 1210 4976 a(\000) p Fn 1301 4976 a(H) p Fj 1377 4990 a(!) p Fp 1427 4976 a(\)) p Fm 1462 4939 a(\000) p Fl(1) p Fp 1557 4976 a(]) p 1608 4976 a(=) p 1704 4976 a(\() p Fn(z) p Fh 1805 4976 a(\000) p Fn 1896 4976 a(H) p Fj 1972 4990 a(!) p Fp 2022 4976 a(\)) p Fm 2057 4939 a(\000) p Fl(1) p Fp 2152 4976 a([) p Fn(A) p Fj 2245 4990 a(n) p Fn 2292 4976 a(;) p 2332 4976 a(H) p Fj 2408 4990 a(!) p Fp 2459 4976 a(]\() p Fn(z) p Fh 2586 4976 a(\000) p Fn 2677 4976 a(H) p Fj 2753 4990 a(!) p Fp 2803 4976 a(\)) p Fm 2838 4939 a(\000) p Fl(1) p Fn 2932 4976 a(:) p Fp 1897 5225 a(34) p eop %%Page: 35 35 35 34 bop 448 573 a @beginspecial @setspecial @endspecial Fp(Since) p Fn 694 573 a(A) p Fj 762 587 a(n) p Fh 848 573 a(!) p Fn 978 573 a(A) p Fp 1085 573 a(in) p Fh 1199 573 a(L) p Fl 1262 540 a(2) p Fp 1302 573 a(,) p 1368 573 a(and) p 1553 573 a(\() p Fn(z) p Fh 1660 573 a(\000) p Fn 1757 573 a(H) p Fj 1833 587 a(!) p Fp 1882 573 a(\)) p Fm 1917 540 a(\000) p Fl(1) p Fp 2051 573 a(is) p 2151 573 a(b) s(ounded) p 2530 573 a(on) p Fn 2665 573 a(l) p Fl 2694 540 a(2) p Fp 2733 573 a(\() p Fk(Z) p 2788 573 a(Z) p Fj 2843 536 a(d) p Fp 2884 573 a(\),) p 2985 573 a(the) p 3150 573 a(LHS) p 3364 573 a(of) 448 697 y(the) p 605 697 a(ab) s(o) m(v) m(e) p 862 697 a(expression) p 1301 697 a(con) m(v) m(erges) p 1708 697 a(to) p 1819 697 a([) p Fn(A;) p Fp 1952 697 a(\() p Fn(z) p Fh 2055 697 a(\000) p Fn 2146 697 a(H) p Fj 2222 711 a(!) p Fp 2271 697 a(\)) p Fm 2306 664 a(\000) p Fl(1) p Fp 2401 697 a(]) p 2457 697 a(in) p Fh 2563 697 a(L) p Fl 2626 664 a(2) p Fp 2695 697 a(as) p Fn 2807 697 a(n) p Fh 2887 697 a(!) p 3003 697 a(1) p Fp(.) p 3159 697 a(On) p 3311 697 a(the) 448 822 y(other) p 695 822 a(hand,) p 959 822 a(trivially) p 1267 822 a(,) p 1332 822 a([) p Fn(A) p Fj 1425 836 a(n) p Fn 1473 822 a(;) p 1513 822 a(H) p Fl 1589 836 a(0) p Fp 1628 822 a(]) p Fh 1694 822 a(!) p Fp 1825 822 a([) p Fn(A;) p 1958 822 a(H) p Fl 2034 836 a(0) p Fp 2074 822 a(],) p 2167 822 a(and) p 2352 822 a(b) m(y) p 2488 822 a(the) p 2654 822 a(construction) p 3184 822 a(of) p Fn 3297 822 a(A) p Fj 3365 836 a(n) p Fp 3412 822 a(,) 448 946 y([) p Fn(A) p Fj 541 960 a(n) p Fn 589 946 a(;) p 629 946 a(V) p Fj 682 960 a(!) p Fp 733 946 a(]) p 783 946 a(=) p Fh 879 946 a(\000L) p Fj 1013 960 a(V) p Ff 1054 968 a(!) p Fp 1102 946 a(\() p Fn(A) p Fj 1205 960 a(n) p Fp 1253 946 a(\)) p Fh 1314 946 a(!) p 1430 946 a(\000L) p Fj 1564 960 a(V) p Ff 1605 968 a(!) p Fp 1653 946 a(\() p Fn(A) p Fp(\)) p 1817 946 a(=) p 1913 946 a([) p Fn(A;) p 2046 946 a(V) p Fj 2099 960 a(!) p Fp 2151 946 a(].) p 2241 946 a(Therefore,) 987 1155 y([) p Fn(A;) p Fp 1120 1155 a(\() p Fn(z) p Fh 1223 1155 a(\000) p Fn 1314 1155 a(H) p Fj 1390 1169 a(!) p Fp 1440 1155 a(\)) p Fm 1475 1118 a(\000) p Fl(1) p Fp 1570 1155 a(]) p 1620 1155 a(=) p 1716 1155 a(\() p Fn(z) p Fh 1818 1155 a(\000) p Fn 1909 1155 a(H) p Fj 1985 1169 a(!) p Fp 2035 1155 a(\)) p Fm 2070 1118 a(\000) p Fl(1) p Fp 2165 1155 a([) p Fn(A;) p 2298 1155 a(H) p Fj 2374 1169 a(!) p Fp 2424 1155 a(]\() p Fn(z) p Fh 2551 1155 a(\000) p Fn 2642 1155 a(H) p Fj 2718 1169 a(!) p Fp 2768 1155 a(\)) p Fm 2803 1118 a(\000) p Fl(1) p Fp 1620 1305 a(=) p 1716 1305 a(0) p Fn(:) 448 1513 y @beginspecial @setspecial @endspecial Fp(By) p 586 1513 a(using) p 819 1513 a(the) p 971 1513 a(almost) p 1259 1513 a(analytic) p 1601 1513 a(con) m(tin) m(uation) p 2121 1513 a(of) p Fn 2220 1513 a(f) p Fj 2265 1528 a(\014) s(;\017) p Ff 2357 1539 a(F) p Fp 2410 1513 a(\() p Fn(\025) p Fp(\)) p 2559 1513 a(\(2.27\)) p 2817 1513 a(whic) m(h) p 3072 1513 a(is) p 3159 1513 a(a) p 3230 1513 a(norm) 448 1638 y(con) m(v) m(ergen) m(t) p 903 1638 a(in) m(tegral,) p 1259 1638 a(w) m(e) p 1393 1638 a(ha) m(v) m(e) 1574 1846 y([) p Fn(A;) p 1707 1846 a(f) p Fj 1752 1861 a(\014) s(;\017) p Ff 1844 1872 a(F) p Fp 1898 1846 a(\() p Fn(H) p Fj 2009 1860 a(!) p Fp 2059 1846 a(\)]) p 2145 1846 a(=) p 2241 1846 a(0) p Fn(:) 448 2055 y @beginspecial @setspecial @endspecial Fp(Let) p Fn 611 2055 a(B) p Fh 710 2055 a(2) p 796 2055 a(A) p Fl 869 2069 a(0) p Fp 908 2055 a(.) p 974 2055 a(By) p 1116 2055 a(Prop) s(osition) p 1606 2055 a(2.5,) p Fn 1259 2264 a(<) p Fp 1355 2264 a([) p Fn(A;) p 1488 2264 a(P) p Fp 1559 2264 a(]) p Fn(;) p 1624 2264 a(B) p 1724 2264 a(>) p Fm 1795 2283 a(L) p Fc 1844 2264 a(2) p Fp 1882 2264 a(=) p Fn(<) p 2049 2264 a(A;) p Fp 2157 2264 a([) p Fn(B) p 2256 2264 a(;) p 2296 2264 a(P) p Fp 2367 2264 a(]) p Fn 2418 2264 a(>) p Fm 2489 2283 a(L) p Fc 2538 2264 a(2) p Fn 2601 2264 a(:) 448 2472 y @beginspecial @setspecial @endspecial Fp(In) p 567 2472 a(step) p 764 2472 a(3) p 844 2472 a(in) p 955 2472 a(the) p 1117 2472 a(pro) s(of) p 1359 2472 a(of) p 1467 2472 a(Prop) s(osition) p 1961 2472 a(2.8,) p 2139 2472 a(w) m(e) p 2278 2472 a(sa) m(w) p Fn 2457 2472 a(f) p Fj 2502 2487 a(\014) s(;\017) p Ff 2594 2498 a(F) p Fp 2648 2472 a(\() p Fn(H) p Fj 2759 2486 a(!) p Fp 2809 2472 a(\)) p Fh 2878 2472 a(!) p Fn 3002 2472 a(P) p Fp 3108 2472 a(in) p Fh 3219 2472 a(L) p Fl 3282 2439 a(2) p Fp 3356 2472 a(as) p Fn 448 2597 a(\014) p Fh 530 2597 a(") p 600 2597 a(1) p Fp(.) p 757 2597 a(Th) m(us) p Fn 1001 2805 a(<) p 1097 2805 a(A;) p Fp 1205 2805 a([) p Fn(B) p 1304 2805 a(;) p 1344 2805 a(P) p Fp 1415 2805 a(]) p Fn 1466 2805 a(>) p Fm 1537 2825 a(L) p Fc 1586 2806 a(2) p Fp 1650 2805 a(=) p 1757 2805 a(lim) p Fj 1745 2865 a(\014) p Fm 1788 2865 a("1) p Fn 1920 2805 a(<) p 2016 2805 a(A;) p Fp 2124 2805 a([) p Fn(B) p 2223 2805 a(;) p 2263 2805 a(f) p Fj 2308 2820 a(\014) s(;\017) p Ff 2400 2831 a(F) p Fp 2454 2805 a(\() p Fn(H) p Fj 2565 2819 a(!) p Fp 2615 2805 a(\)]) p Fn 2701 2805 a(>) p Fm 2772 2825 a(L) p Fc 2821 2806 a(2) p Fp 1650 2988 a(=) p 1757 2988 a(lim) p Fj 1745 3048 a(\014) p Fm 1788 3048 a("1) p Fn 1920 2988 a(<) p Fp 2016 2988 a([) p Fn(A;) p 2149 2988 a(f) p Fj 2194 3003 a(\014) s(;\017) p Ff 2286 3014 a(F) p Fp 2340 2988 a(\() p Fn(H) p Fj 2451 3002 a(!) p Fp 2501 2988 a(\)]) p Fn(;) p 2601 2988 a(B) p 2701 2988 a(>) p Fm 2772 3008 a(L) p Fc 2821 2989 a(2) p Fp 1650 3161 a(=) p 1745 3161 a(0) p Fn(:) 448 3370 y @beginspecial @setspecial @endspecial Fp(Therefore,) p 886 3370 a([) p Fn(A;) p 1019 3370 a(P) p Fp 1090 3370 a(]) p 1141 3370 a(=) p 1237 3370 a(0.) p 1348 3306 60 4 v 1348 3394 4 89 v 1404 3394 V 1348 3397 60 4 v 448 3619 a @beginspecial @setspecial @endspecial(W) p 533 3619 a(e) p 605 3619 a(are) p 757 3619 a(ready) p 1007 3619 a(to) p 1118 3619 a(pro) m(v) m(e) p 1363 3619 a(Theorem) p 1747 3619 a(1.) 589 3743 y @beginspecial @setspecial @endspecial Fo(Pr) p 684 3743 a(o) p 725 3743 a(of) p 833 3743 a(of) p 940 3743 a(The) p 1088 3743 a(or) p 1167 3743 a(em) p 1318 3743 a(1) 589 3868 y @beginspecial @setspecial @endspecial Fp(By) p 732 3868 a(Lemma) p 1057 3868 a(3.2,) p 1228 3868 a(w) m(e) p 1362 3868 a(ha) m(v) m(e) p Fn 937 4076 a(\033) p Fl 989 4090 a(2) p Fp 1029 4076 a(\() p Fn(!) s(;) p 1164 4076 a(\017) p Fj 1201 4090 a(F) p Fp 1260 4076 a(\)) p 1320 4076 a(=) p 1416 4076 a(lim) p Fj 1427 4136 a(\016) p Fm 1460 4136 a(#) p Fl(0) p Fn 1558 4076 a(i) p 1614 4076 a(<) p Fp 1710 4076 a(\() p Fh(\000) p Fn(i\016) p Fh 1912 4076 a(\000) p 2002 4076 a(L) p Fj 2065 4090 a(H) p Ff 2123 4098 a(!) p Fp 2172 4076 a(\)) p Fm 2207 4039 a(\000) p Fl(1) p Fn 2302 4076 a(@) p Fl 2350 4090 a(1) p Fn 2389 4076 a(H) p Fj 2465 4090 a(!) p Fn 2515 4076 a(;) p 2555 4076 a(@) p Fl 2603 4090 a(1) p Fn 2644 4076 a(P) p 2740 4076 a(>) p Fm 2811 4096 a(L) p Fc 2860 4077 a(2) p Fn 2923 4076 a(:) 448 4313 y @beginspecial @setspecial @endspecial Fp(By) p 591 4313 a(Lemma) p 915 4313 a(3.4,) p 1087 4313 a(Prop) s(osition) p 1577 4313 a(2.5,) p 1748 4313 a(and) p 1925 4313 a(Lemma) p 2250 4313 a(3.6,) p Fn 557 4522 a(i) p 634 4522 a(<) p Fp 730 4522 a(\() p Fh(\000) p Fn(i\016) p Fh 931 4522 a(\000) p 1022 4522 a(L) p Fj 1085 4536 a(H) p Ff 1143 4544 a(!) p Fp 1192 4522 a(\)) p Fm 1227 4484 a(\000) p Fl(1) p Fn 1321 4522 a(@) p Fl 1369 4536 a(1) p Fn 1409 4522 a(H) p Fj 1485 4536 a(!) p Fn 1535 4522 a(;) p 1575 4522 a(@) p Fl 1623 4536 a(1) p Fn 1663 4522 a(P) p 1759 4522 a(>) p Fm 1830 4541 a(L) p Fc 1879 4522 a(2) p Fp 538 4671 a(=) p Fn 634 4671 a(i) p 690 4671 a(<) p Fp 786 4671 a(\() p Fh(\000) p Fn(i\016) p Fh 988 4671 a(\000) p 1079 4671 a(L) p Fj 1142 4685 a(H) p Ff 1200 4693 a(!) p Fp 1248 4671 a(\)) p Fm 1283 4634 a(\000) p Fl(1) p Fn 1378 4671 a(@) p Fl 1426 4685 a(1) p Fn 1466 4671 a(H) p Fj 1542 4685 a(!) p Fn 1592 4671 a(;) p 1632 4671 a(P) p Fp 1703 4671 a(\() p Fn(@) p Fl 1786 4685 a(1) p Fn 1826 4671 a(P) p Fp 1897 4671 a(\)) p Fn(Q) p Fp 2024 4671 a(+) p Fn 2115 4671 a(Q) p Fp(\() p Fn(@) p Fl 2270 4685 a(1) p Fn 2310 4671 a(P) p Fp 2381 4671 a(\)) p Fn(P) p 2513 4671 a(>) p Fm 2584 4691 a(L) p Fc 2633 4672 a(2) p Fp 538 4821 a(=) p Fn 634 4821 a(i) p 690 4821 a(<) p 786 4821 a(P) p Fh 857 4821 a(f) p Fp(\() p Fh(\000) p Fn(i\016) p Fh 1104 4821 a(\000) p 1195 4821 a(L) p Fj 1258 4835 a(H) p Ff 1316 4843 a(!) p Fp 1365 4821 a(\)) p Fm 1400 4783 a(\000) p Fl(1) p Fn 1494 4821 a(@) p Fl 1542 4835 a(1) p Fn 1582 4821 a(H) p Fj 1658 4835 a(!) p Fh 1708 4821 a(g) p Fn(Q) p Fp 1845 4821 a(+) p Fn 1936 4821 a(Q) p Fh(f) p Fp(\() p Fh(\000) p Fn(i\016) p Fh 2255 4821 a(\000) p 2346 4821 a(L) p Fj 2409 4835 a(H) p Ff 2467 4843 a(!) p Fp 2516 4821 a(\)) p Fm 2551 4783 a(\000) p Fl(1) p Fn 2645 4821 a(@) p Fl 2693 4835 a(1) p Fn 2733 4821 a(H) p Fj 2809 4835 a(!) p Fh 2859 4821 a(g) p Fn(P) s(;) p 3005 4821 a(@) p Fl 3053 4835 a(1) p Fn 3093 4821 a(P) p 3190 4821 a(>) p Fm 3261 4840 a(L) p Fc 3310 4821 a(2) p Fp 538 4970 a(=) p Fn 634 4970 a(i) p 690 4970 a(<) p Fp 786 4970 a(\() p Fh(\000) p Fn(i\016) p Fh 988 4970 a(\000) p 1079 4970 a(L) p Fj 1142 4984 a(H) p Ff 1200 4992 a(!) p Fp 1248 4970 a(\)) p Fm 1283 4932 a(\000) p Fl(1) p Fi 1378 4876 a(\020) p Fn 1427 4970 a(P) p Fp 1498 4970 a(\() p Fn(@) p Fl 1581 4984 a(1) p Fn 1621 4970 a(H) p Fj 1697 4984 a(!) p Fp 1747 4970 a(\)) p Fn(Q) p Fp 1875 4970 a(+) p Fn 1966 4970 a(Q) p Fp(\() p Fn(@) p Fl 2121 4984 a(1) p Fn 2161 4970 a(H) p Fj 2237 4984 a(!) p Fp 2287 4970 a(\)) p Fn(P) p Fi 2393 4876 a(\021) p Fn 2443 4970 a(;) p 2483 4970 a(@) p Fl 2531 4984 a(1) p Fn 2571 4970 a(P) p 2667 4970 a(>) p Fm 2738 4990 a(L) p Fc 2787 4971 a(2) p Fn 2850 4970 a(:) p Fp 1897 5225 a(35) p eop %%Page: 36 36 36 35 bop 448 573 a @beginspecial @setspecial @endspecial Fp(As) p 573 573 a(functions) p 955 573 a(on) p 1071 573 a(\012) p Fh(\002) p Fk(Z) p 1228 573 a(Z) p Fj 1283 536 a(d) p Fh 1323 573 a(\002) p Fk(Z) p 1414 573 a(Z) p Fj 1469 536 a(d) p Fp 1509 573 a(,) p 1557 573 a(w) m(e) p 1681 573 a(ha) m(v) m(e) p 1881 573 a(\() p Fn(@) p Fl 1964 587 a(1) p Fn 2004 573 a(H) p Fj 2080 587 a(!) p Fp 2130 573 a(\)\() p Fn(!) p Fp 2275 573 a(;) p Fn 2315 573 a(x;) p 2407 573 a(y) p Fp 2455 573 a(\)) p 2516 573 a(=) p Fh 2612 573 a(\000) p Fp(\() p Fh(L) p Fj 2781 587 a(H) p Ff 2839 595 a(!) p Fp 2888 573 a(\() p Fn(x) p Fl 2975 587 a(1) p Fp 3015 573 a(\)\)\() p Fn(!) p Fp 3196 573 a(;) p Fn 3236 573 a(x;) p 3328 573 a(y) p Fp 3376 573 a(\).) 448 697 y(T) p 506 697 a(ogether) p 830 697 a(with) p 1037 697 a(Lemma) p 1361 697 a(3.8,) p Fn 847 899 a(i) p 923 899 a(<) p Fp 1019 899 a(\() p Fh(\000) p Fn(i\016) p Fh 1221 899 a(\000) p 1312 899 a(L) p Fj 1375 913 a(H) p Ff 1433 921 a(!) p Fp 1481 899 a(\)) p Fm 1516 862 a(\000) p Fl(1) p Fi 1611 805 a(\020) p Fn 1661 899 a(P) p Fp 1732 899 a(\() p Fn(@) p Fl 1815 913 a(1) p Fn 1855 899 a(H) p Fj 1931 913 a(!) p Fp 1981 899 a(\)) p Fn(Q) p Fp 2108 899 a(+) p Fn 2199 899 a(Q) p Fp(\() p Fn(@) p Fl 2354 913 a(1) p Fn 2394 899 a(H) p Fj 2470 913 a(!) p Fp 2520 899 a(\)) p Fn(P) p Fi 2626 805 a(\021) p Fn 2676 899 a(;) p 2716 899 a(@) p Fl 2764 913 a(1) p Fn 2804 899 a(P) p 2900 899 a(>) p Fm 2971 919 a(L) p Fc 3020 900 a(2) p Fp 827 1065 a(=) p 923 1065 a(\() p Fh(\000) p Fn(i) p Fp(\)) p Fn 1121 1065 a(<) p Fp 1217 1065 a(\() p Fh(\000) p Fn(i\016) p Fh 1419 1065 a(\000) p 1510 1065 a(L) p Fj 1573 1079 a(H) p Ff 1631 1087 a(!) p Fp 1679 1065 a(\)) p Fm 1714 1027 a(\000) p Fl(1) p Fh 1809 1065 a(L) p Fj 1872 1079 a(H) p Ff 1930 1087 a(!) p Fp 1979 1065 a(\() p Fn(Qx) p Fl 2138 1079 a(1) p Fn 2177 1065 a(P) p Fp 2268 1065 a(+) p Fn 2359 1065 a(P) p 2430 1065 a(x) p Fl 2482 1079 a(1) p Fn 2522 1065 a(Q) p Fp(\)) p Fn(;) p 2669 1065 a(@) p Fl 2717 1079 a(1) p Fn 2757 1065 a(P) p 2853 1065 a(>) p Fm 2924 1084 a(L) p Fc 2973 1066 a(2) p Fn 3036 1065 a(:) 448 1267 y @beginspecial @setspecial @endspecial Fp(By) p 613 1267 a(direct) p 892 1267 a(computation,) p Fi 1475 1172 a(h) p Fp 1514 1267 a([) p Fn(x) p Fl 1591 1281 a(1) p Fn 1631 1267 a(;) p 1671 1267 a(P) p Fp 1742 1267 a(]) p Fn(;) p 1807 1267 a(P) p Fi 1878 1172 a(i) p Fh 1980 1267 a(2) p 2102 1267 a(D) p Fp 2175 1267 a(\() p Fh(L) p Fj 2273 1281 a(H) p Ff 2331 1289 a(!) p Fp 2380 1267 a(\),) p 2498 1267 a(and) p Fn 2696 1267 a(Qx) p Fl 2820 1281 a(1) p Fn 2859 1267 a(P) p Fp 2965 1267 a(+) p Fn 3071 1267 a(P) p 3142 1267 a(x) p Fl 3194 1281 a(1) p Fn 3233 1267 a(Q) p Fp 3366 1267 a(=) p Fi 448 1330 a(h) p Fp 488 1424 a([) p Fn(x) p Fl 565 1438 a(1) p Fn 604 1424 a(;) p 644 1424 a(P) p Fp 715 1424 a(]) p Fn(;) p 780 1424 a(P) p Fi 851 1330 a(i) p Fp 891 1424 a(.) p 957 1424 a(By) p 1100 1424 a(Lemma) p 1424 1424 a(3.9) p 1571 1424 a(and) p 1747 1424 a(\(3.10\),) p 2035 1424 a(w) m(e) p 2169 1424 a(compute) p Fn 939 1642 a(i) p 1015 1642 a(<) p Fp 1111 1642 a(\() p Fh(\000) p Fn(i\016) p Fh 1312 1642 a(\000) p 1403 1642 a(L) p Fj 1466 1656 a(H) p Ff 1524 1664 a(!) p Fp 1573 1642 a(\)) p Fm 1608 1605 a(\000) p Fl(1) p Fn 1703 1642 a(@) p Fl 1751 1656 a(1) p Fn 1790 1642 a(H) p Fj 1866 1656 a(!) p Fn 1916 1642 a(;) p 1956 1642 a(@) p Fl 2004 1656 a(1) p Fn 2044 1642 a(P) p 2141 1642 a(>) p Fm 2212 1662 a(L) p Fc 2261 1643 a(2) p Fp 919 1792 a(=) p 1015 1792 a(\() p Fh(\000) p Fn(i) p Fp(\)) p Fn 1213 1792 a(<) p Fp 1309 1792 a(\() p Fh(\000) p Fn(i\016) p Fh 1510 1792 a(\000) p 1601 1792 a(L) p Fj 1664 1806 a(H) p Ff 1722 1814 a(!) p Fp 1771 1792 a(\)) p Fm 1806 1754 a(\000) p Fl(1) p Fh 1901 1792 a(L) p Fj 1964 1806 a(H) p Ff 2022 1814 a(!) p Fp 2070 1792 a(\() p Fi 2105 1698 a(h) p Fp 2145 1792 a([) p Fn(x) p Fl 2222 1806 a(1) p Fn 2261 1792 a(;) p 2301 1792 a(P) p Fp 2372 1792 a(]) p Fn(;) p 2437 1792 a(P) p Fi 2508 1698 a(i) p Fp 2549 1792 a(\)) p Fn(;) p 2624 1792 a(@) p Fl 2672 1806 a(1) p Fn 2712 1792 a(P) p 2808 1792 a(>) p Fm 2879 1811 a(L) p Fc 2928 1793 a(2) p Fh 1015 1974 a(\000) p 1071 1974 a(!) p Fn 1187 1974 a(i) p 1243 1974 a(<) p Fi 1339 1880 a(h) p Fp 1378 1974 a([) p Fn(x) p Fl 1455 1988 a(1) p Fn 1495 1974 a(;) p 1535 1974 a(P) p Fp 1606 1974 a(]) p Fn(;) p 1671 1974 a(P) p Fi 1742 1880 a(i) p Fn 1782 1974 a(;) p 1822 1974 a(@) p Fl 1870 1988 a(1) p Fn 1910 1974 a(P) p 2007 1974 a(>) p Fm 2078 1994 a(L) p Fc 2127 1975 a(2) p Fp 2281 1974 a(\() p Fn(\016) p Fh 2385 1974 a(#) p Fp 2456 1974 a(0\)) 919 2124 y(=) p Fn 1015 2124 a(i) p 1072 2124 a(<) p Fp 1168 2124 a([) p Fn(@) p Fl 1241 2138 a(1) p Fn 1281 2124 a(P) s(;) p 1382 2124 a(P) p Fp 1453 2124 a(]) p Fn(;) p 1518 2124 a(@) p Fl 1566 2138 a(1) p Fn 1606 2124 a(P) p 1702 2124 a(>) p Fm 1773 2144 a(L) p Fc 1822 2125 a(2) p Fp 919 2273 a(=) p Fn 1015 2273 a(i) p 1072 2273 a(<) p Fp 1168 2273 a(\() p Fn(@) p Fl 1251 2287 a(1) p Fn 1291 2273 a(P) p Fp 1362 2273 a(\)) p Fn(P) s(;) p 1498 2273 a(@) p Fl 1546 2287 a(1) p Fn 1586 2273 a(P) p 1682 2273 a(>) p Fm 1753 2293 a(L) p Fc 1802 2274 a(2) p Fh 1865 2273 a(\000) p Fn(i) p 1993 2273 a(<) p 2089 2273 a(P) p Fp 2160 2273 a(\() p Fn(@) p Fl 2243 2287 a(1) p Fn 2283 2273 a(P) p Fp 2354 2273 a(\)) p Fn(;) p 2429 2273 a(@) p Fl 2477 2287 a(1) p Fn 2517 2273 a(P) p 2613 2273 a(>) p Fm 2684 2293 a(L) p Fc 2733 2274 a(2) p Fn 2797 2273 a(:) 448 2475 y @beginspecial @setspecial @endspecial Fp(By) p 591 2475 a(Prop) s(ositions) p 1116 2475 a(2.2,) p 1288 2475 a(2.4,) p Fn 1048 2677 a(<) p Fp 1144 2677 a(\() p Fn(@) p Fl 1227 2691 a(1) p Fn 1267 2677 a(P) p Fp 1338 2677 a(\)) p Fn(P) s(;) p 1474 2677 a(@) p Fl 1522 2691 a(1) p Fn 1562 2677 a(P) p 1658 2677 a(>) p Fm 1729 2697 a(L) p Fc 1778 2678 a(2) p Fp 1842 2677 a(=) p Fh 1938 2677 a(\000T) p Fp 2081 2677 a(\() p Fn(P) p Fp 2187 2677 a(\() p Fn(@) p Fl 2270 2691 a(1) p Fn 2310 2677 a(P) p Fp 2381 2677 a(\)\() p Fn(@) p Fl 2499 2691 a(1) p Fn 2540 2677 a(P) p Fp 2611 2677 a(\)\)) 1842 2826 y(=) p Fh 1938 2826 a(\000T) p Fp 2081 2826 a(\(\() p Fn(@) p Fl 2199 2840 a(1) p Fn 2239 2826 a(P) p Fp 2310 2826 a(\)) p Fn(P) p Fp 2416 2826 a(\() p Fn(@) p Fl 2499 2840 a(1) p Fn 2540 2826 a(P) p Fp 2611 2826 a(\)\)) 1842 2976 y(=) p Fn 1938 2976 a(<) p 2034 2976 a(P) p Fp 2105 2976 a(\() p Fn(@) p Fl 2188 2990 a(1) p Fn 2228 2976 a(P) p Fp 2299 2976 a(\)) p Fn(;) p Fp 2374 2976 a(\() p Fn(@) p Fl 2457 2990 a(1) p Fn 2497 2976 a(P) p Fp 2568 2976 a(\)) p Fn 2629 2976 a(>) p Fm 2700 2996 a(L) p Fc 2749 2977 a(2) p Fn 2812 2976 a(:) 448 3178 y @beginspecial @setspecial @endspecial Fp(Therefore,) p 886 3178 a(w) m(e) p 1020 3178 a(pro) m(v) m(ed) p Fn 1315 3178 a(\033) p Fl 1367 3192 a(2) p Fp 1407 3178 a(\() p Fn(!) s(;) p 1542 3178 a(\017) p Fj 1579 3192 a(F) p Fp 1638 3178 a(\)) p 1698 3178 a(=) p 1794 3178 a(0,) p 1895 3178 a(for) p 2034 3178 a(a.e.) p Fn 2211 3178 a(!) p Fp 2271 3178 a(.) p 2337 3114 60 4 v 2337 3203 4 89 v 2392 3203 V 2337 3206 60 4 v Fq 448 3462 a(4) p 650 3462 a(Pro) t(of) p 1021 3462 a(of) p 1174 3462 a(Theorem) p 1744 3462 a(2) 448 3676 y @beginspecial @setspecial @endspecial Fp(The) p 638 3676 a(follo) m(wing) p 1024 3676 a(prop) s(osition) p 1505 3676 a(is) p 1599 3676 a(imp) s(ortan) m(t) p 2031 3676 a(to) p 2144 3676 a(study) p Fh 2397 3676 a(E) p 2483 3676 a(#) p Fp 2558 3676 a(0) p 2636 3676 a(limit) p 2856 3676 a(in) p 2965 3676 a(the) p 3124 3676 a(pro) s(of) p 3364 3676 a(of) 448 3801 y(Theorem) p 832 3801 a(2.) p Fe 448 3989 a(Prop) s(osition) p 1014 3989 a(4.1) p 1193 3989 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1288 3989 a(A) p Fh 1381 3989 a(2) p 1467 3989 a(L) p Fl 1530 3956 a(2) p Fo 1602 3989 a(satis\014es) p Fn 1435 4190 a(A) p Fh 1528 4190 a(2) p 1614 4190 a(D) p Fp 1687 4190 a(\() p Fh(L) p Fj 1785 4204 a(H) p Ff 1843 4212 a(!) p Fp 1892 4190 a(\)) p Fn(;) p Fp 448 4190 a(\(4.1\)) p Fn 1435 4340 a(e) p Fj 1477 4302 a(it) p Fm(L) p Ff 1575 4313 a(H) 1625 4321 y(!) p Fn 1678 4340 a(A) p Fh 1772 4340 a(2) p 1858 4340 a(D) p Fp 1931 4340 a(\() p Fn(@) p Fl 2014 4354 a(1) p Fp 2053 4340 a(\)) p Fn(;) p 2222 4340 a(t) p Fh 2280 4340 a(2) p Fp 2366 4340 a(I) p 2384 4340 a(R) p Fn 2450 4340 a(;) p Fp 448 4340 a(\(4.2\)) 448 4542 y @beginspecial @setspecial @endspecial Fo(Then,) p 713 4542 a(we) p 848 4542 a(have) p 1057 4542 a(the) p 1208 4542 a(fol) p 1310 4542 a(lowing) p 1594 4542 a(\\Duhamel") p 2069 4542 a(formula) p 2407 4542 a(for) p Fn 2553 4542 a(e) p Fj 2595 4494 a(it) p Fm(L) p Ff 2693 4505 a(H) 2743 4522 y(!) r(;) p Fd(E) p Fo 2885 4542 a(and) p Fn 3061 4542 a(e) p Fj 3103 4509 a(it) p Fm(L) p Ff 3201 4520 a(H) 3251 4528 y(!) p Fn 830 4774 a(e) p Fj 872 4727 a(it) p Fm(L) p Ff 970 4738 a(H) 1020 4755 y(!) r(;) p Fd(E) p Fn 1130 4774 a(A) p Fh 1218 4774 a(\000) p Fn 1309 4774 a(e) p Fj 1351 4737 a(it) p Fm(L) p Ff 1449 4748 a(H) 1499 4756 y(!) p Fn 1552 4774 a(A) p Fp 1646 4774 a(=) p Fn 1742 4774 a(i) p Fh(E) p Fi 1844 4660 a(Z) p Fj 1927 4686 a(t) p Fl 1890 4848 a(0) p Fn 1972 4774 a(ds) p 2087 4774 a(e) p Fj 2129 4727 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 2369 4738 a(H) 2419 4755 y(!) r(;) p Fd(E) p Fp 2529 4774 a([) p Fn(x) p Fl 2606 4788 a(1) p Fn 2646 4774 a(;) p 2686 4774 a(e) p Fj 2728 4737 a(is) p Fm(L) p Ff 2834 4748 a(H) 2884 4756 y(!) p Fn 2937 4774 a(A) p Fp(]) p Fn(:) p Fp 1897 5225 a(36) p eop %%Page: 37 37 37 36 bop 448 573 a @beginspecial @setspecial @endspecial Fo(Pr) p 543 573 a(o) p 584 573 a(of.) p Fp 790 573 a(By) p 953 573 a(\(4.1\),) p 1221 573 a(\(4.2\),) p Fn 1489 573 a(e) p Fj 1531 540 a(is) p Fm(L) p Ff 1637 551 a(H) 1687 559 y(!) p Fn 1739 573 a(A) p Fh 1867 573 a(2) p 1987 573 a(D) p Fp 2060 573 a(\() p Fh(L) p Fj 2158 587 a(H) p Ff 2216 595 a(!) p Fp 2264 573 a(\),) p Fn 2381 573 a(e) p Fj 2423 540 a(is) p Fm(L) p Ff 2529 551 a(H) 2579 559 y(!) p Fn 2631 573 a(A) p Fh 2759 573 a(2) p 2879 573 a(D) p Fp 2952 573 a(\() p Fn(@) p Fl 3035 587 a(1) p Fp 3075 573 a(\).) p 3237 573 a(Th) m(us) p Fn 448 697 a(e) p Fj 490 664 a(is) p Fm(L) p Ff 596 675 a(H) 646 683 y(!) p Fn 699 697 a(A) p Fh 792 697 a(2) p 878 697 a(D) p Fp 951 697 a(\() p Fh(L) p Fj 1049 711 a(H) p Ff 1107 722 a(!) r(;) p Fd(E) p Fp 1212 697 a(\),) p 1303 697 a(and) p Fn 1480 697 a(e) p Fm 1522 650 a(\000) p Fj(is) p Fm(L) p Ff 1683 661 a(H) 1733 678 y(!) r(;) p Fd(E) p Fn 1841 697 a(e) p Fj 1883 664 a(is) p Fm(L) p Ff 1989 675 a(H) 2039 683 y(!) p Fn 2092 697 a(A) p Fp 2190 697 a(is) p 2282 697 a(di\013eren) m(tiable) p 2827 697 a(w.r.t.) p Fn 3080 697 a(s) p Fp(.) p Fn 805 954 a(e) p Fm 847 907 a(\000) p Fj(it) p Fm(L) p Ff 1000 918 a(H) 1050 935 y(!) r(;) p Fd(E) p Fn 1160 954 a(e) p Fj 1202 917 a(it) p Fm(L) p Ff 1300 928 a(H) 1350 936 y(!) p Fn 1403 954 a(A) p Fh 1491 954 a(\000) p Fn 1582 954 a(A) p Fp 1676 954 a(=) p Fi 1772 840 a(Z) p Fj 1855 866 a(t) p Fl 1818 1028 a(0) p Fn 1899 954 a(ds) 2046 893 y(d) p 2025 933 90 4 v 2025 1017 a(ds) p Fi 2124 860 a(\020) p Fn 2174 954 a(e) p Fm 2216 907 a(\000) p Fj(is) p Fm(L) p Ff 2377 918 a(H) 2427 935 y(!) r(;) p Fd(E) p Fn 2536 954 a(e) p Fj 2578 917 a(is) p Fm(L) p Ff 2684 928 a(H) 2734 936 y(!) p Fn 2786 954 a(A) p Fi 2854 860 a(\021) p Fp 1676 1191 a(=) p Fh 1772 1191 a(\000) p Fn(i) p Fh(E) p Fi 1945 1076 a(Z) p Fj 2028 1102 a(t) p Fl 1991 1265 a(0) p Fn 2073 1191 a(ds) p 2188 1191 a(e) p Fm 2230 1143 a(\000) p Fj(is) p Fm(L) p Ff 2391 1154 a(H) 2441 1171 y(!) r(;) p Fd(E) p Fn 2550 1191 a(@) p Fl 2598 1205 a(1) p Fi 2637 1097 a(\020) p Fn 2687 1191 a(e) p Fj 2729 1153 a(is) p Fm(L) p Ff 2835 1164 a(H) 2885 1172 y(!) p Fn 2937 1191 a(A) p Fi 3005 1097 a(\021) p Fn 3055 1191 a(:) 448 1450 y @beginspecial @setspecial @endspecial Fp(By) p 593 1450 a(m) m(ultiplying) p Fn 1080 1450 a(e) p Fj 1122 1403 a(it) p Fm(L) p Ff 1220 1414 a(H) 1270 1431 y(!) r(;) p Fd(E) p Fp 1412 1450 a(from) p 1630 1450 a(the) p 1788 1450 a(righ) m(t) p 2010 1450 a(on) p 2139 1450 a(b) s(oth) p 2356 1450 a(sides,) p 2602 1450 a(w) m(e) p 2738 1450 a(arriv) m(e) p 2998 1450 a(at) p 3112 1450 a(the) p 3270 1450 a(con-) 448 1575 y(clusion.) p 787 1511 60 4 v 787 1600 4 89 v 843 1600 V 787 1603 60 4 v Fe 448 1824 a(Lemma) p 819 1824 a(4.1) p 998 1824 a @beginspecial @setspecial @endspecial Fo(\(1\)) p Fn 1151 1824 a(@) p Fl 1199 1838 a(1) p Fn 1239 1824 a(H) p Fj 1315 1838 a(!) p Fo 1398 1824 a(satis\014es) p 1739 1824 a(\(4.1\),) p 1995 1824 a(\(4.2\),) 589 1948 y @beginspecial @setspecial @endspecial(\(2\)) p Fp 743 1948 a([) p Fn(x) p Fl 820 1962 a(1) p Fn 859 1948 a(;) p 899 1948 a(e) p Fj 941 1915 a(is) p Fm(L) p Ff 1047 1926 a(H) 1097 1934 y(!) p Fp 1150 1948 a(\() p Fn(@) p Fl 1233 1962 a(1) p Fn 1273 1948 a(H) p Fj 1349 1962 a(!) p Fp 1399 1948 a(\)]) p Fo 1492 1948 a(satis\014es) p 1834 1948 a(\(4.1\),) p 2089 1948 a(\(4.2\).) 448 2165 y @beginspecial @setspecial @endspecial Fp(T) p 506 2165 a(o) p 582 2165 a(pro) m(v) m(e) p 827 2165 a(Lemma) p 1152 2165 a(4.1,) p 1324 2165 a(w) m(e) p 1457 2165 a(use) p 1614 2165 a(the) p 1771 2165 a(follo) m(wing) p 2155 2165 a(estimate.) p Fe 448 2359 a(Theorem) p 892 2359 a(4.1) p 1071 2359 a @beginspecial @setspecial @endspecial Fo(\(The) p 1256 2359 a(or) p 1335 2359 a(em) p 1481 2359 a(3) p 1555 2359 a(in) p 1662 2359 a([2]\)) p 1829 2359 a(L) p 1881 2359 a(et) p Fn 1981 2359 a(F) p Fo 2079 2359 a(b) p 2116 2359 a(e) p 2186 2359 a(a) p 2260 2359 a(function) p 2613 2359 a(analytic) p 2952 2359 a(and) p 3123 2359 a(b) p 3160 2359 a(ounde) p 3389 2359 a(d) 448 2483 y(on) p 578 2483 a(a) p 657 2483 a(strip) p Fn 870 2483 a(S) p Fj 926 2497 a(\021) p Fp 993 2483 a(:=) p Fh 1114 2483 a(f) p Fn(z) p Fh 1231 2483 a(2) p 1343 2479 4 56 v Fp 1317 2483 a(C) p 1423 2483 a(:) p Fh 1489 2483 a(j) p Fo(Im) p Fn 1656 2483 a(z) p Fh 1702 2483 a(j) p Fn 1753 2483 a(<) p 1849 2483 a(\021) p Fh 1897 2483 a(g) p Fo(.) p 2012 2483 a(Then,) p Fh 1165 2692 a(j) p Fn(F) p Fp 1261 2692 a(\() p Fn(H) p Fj 1372 2706 a(!) p Fp 1423 2692 a(\)\() p Fn(!) p Fp 1569 2692 a(;) p Fn 1609 2692 a(x;) p 1701 2692 a(y) p Fp 1749 2692 a(\)) p Fh(j) p 1835 2692 a(\024) p Fp 1931 2692 a(18) p Fh 2021 2613 a(p) p 2098 2613 46 4 v Fp 2098 2692 a(2) p Fh(k) p Fn(F) p Fh 2259 2692 a(k) p Fm 2304 2706 a(1) p Fn 2380 2692 a(e) p Fm 2422 2655 a(\000) p Fj(\026) p Fm(j) p Fj(x) p Fm(\000) p Fj(y) p Fm 2671 2655 a(j) p Fn 2695 2692 a(;) p Fp 448 2692 a(\(4.3\)) 448 2901 y @beginspecial @setspecial @endspecial Fo(for) p 599 2901 a(any) p Fn 780 2901 a(\026) p 871 2901 a(>) p Fp 977 2901 a(0) p Fo 1061 2901 a(such) p 1274 2901 a(that) p 1466 2901 a(the) p 1623 2901 a(ine) p 1739 2901 a(quality) p Fi 2040 2837 a(P) p Fm 2128 2924 a(j) p Fj(x) p Fm(j) p Fl(=1) p Fp 2301 2901 a(\() p Fn(e) p Fj 2378 2868 a(\026) p Fm(j) p Fj(x) p Fm(j) p Fh 2529 2901 a(\000) p Fp 2624 2901 a(1\)) p Fh 2741 2901 a(\024) p Fn 2848 2901 a(\021) s(=) p Fp(2) p Fo 3025 2901 a(holds,) p 3293 2901 a(and) p Fh 448 3026 a(k) p Fn(F) p Fh 564 3026 a(k) p Fm 609 3040 a(1) p Fp 710 3026 a(:=) p 831 3026 a(sup) p Fj 968 3048 a(z) p Fm 1004 3048 a(2) p Fj(S) p Ff 1094 3056 a(\021) p Fh 1151 3026 a(j) p Fn(F) p Fp 1247 3026 a(\() p Fn(z) p Fp 1328 3026 a(\)) p Fh(j) p Fo(.) 448 3219 y @beginspecial @setspecial @endspecial Fp(W) p 533 3219 a(e) p 605 3219 a(will) p 777 3219 a(mak) m(e) p 1015 3219 a(use) p 1172 3219 a(of) p 1276 3219 a(the) p 1433 3219 a(fact) p 1613 3219 a(that) p 1810 3219 a(the) p 1967 3219 a(b) s(ound) p 2248 3219 a(in) p 2354 3219 a(\(4.3\)) p 2572 3219 a(holds) p 2810 3219 a(uniformly) p 3225 3219 a(w.r.t.) p Fn 448 3344 a(!) p Fh 533 3344 a(2) p Fp 619 3344 a(\012.) 589 3468 y @beginspecial @setspecial @endspecial Fo(Pr) p 684 3468 a(o) p 725 3468 a(of) p 848 3468 a(of) p 969 3468 a(L) p 1021 3468 a(emma) p 1305 3468 a(4.1) p Fp 1472 3468 a(\(1\)) p 1634 3468 a(Since) p Fn 1887 3468 a(@) p Fl 1935 3482 a(1) p Fn 1974 3468 a(H) p Fj 2050 3482 a(!) p Fh 2151 3468 a(2) p 2263 3468 a(A) p Fl 2336 3482 a(0) p Fp 2375 3468 a(,) p 2450 3468 a(and) p Fn 2642 3468 a(H) p Fj 2718 3482 a(!) p Fh 2820 3468 a(2) p 2931 3468 a(L) p Fl 2994 3435 a(2) p Fp 3033 3468 a(,) p 3108 3468 a(w) m(e) p 3258 3468 a(ha) m(v) m(e) p Fh 448 3593 a(L) p Fj 511 3607 a(H) p Ff 569 3615 a(!) p Fp 618 3593 a(\() p Fn(@) p Fl 701 3607 a(1) p Fn 741 3593 a(H) p Fj 817 3607 a(!) p Fp 867 3593 a(\)) p Fh 928 3593 a(2) p 1013 3593 a(L) p Fl 1076 3560 a(2) p Fp 1116 3593 a(.) p 1181 3593 a(Hence) p Fn 1450 3593 a(@) p Fl 1498 3607 a(1) p Fn 1538 3593 a(H) p Fj 1614 3607 a(!) p Fh 1689 3593 a(2) p 1775 3593 a(D) p Fp 1848 3593 a(\() p Fh(L) p Fj 1946 3607 a(H) p Ff 2004 3615 a(!) p Fp 2052 3593 a(\).) p 2153 3593 a(By) p 2295 3593 a(\(4.3\),) p 2536 3593 a(for) p 2674 3593 a(an) m(y) p 2845 3593 a(\014xed) p Fn 3064 3593 a(\021) p 3137 3593 a(>) p Fp 3233 3593 a(0,) p 3334 3593 a(w) m(e) 448 3717 y(ha) m(v) m(e) p Fh 1244 3842 a(j) p Fn(e) p Fj 1311 3804 a(itH) p Ff 1418 3812 a(!) p Fp 1468 3842 a(\() p Fn(!) p Fp 1578 3842 a(;) p Fn 1618 3842 a(x;) p 1710 3842 a(y) p Fp 1758 3842 a(\)) p Fh(j) p 1845 3842 a(\024) p Fp 1940 3842 a(18) p Fh 2030 3762 a(p) p 2107 3762 V Fp 2107 3842 a(2) p Fn 2153 3842 a(e) p Fj 2195 3804 a(\021) p Fm 2232 3804 a(j) p Fj(t) p Fm(j) p Fn 2302 3842 a(e) p Fm 2344 3804 a(\000) p Fj(\026) p Fm(j) p Fj(x) p Fm(\000) p Fj(y) p Fm 2593 3804 a(j) p Fn 2616 3842 a(;) p Fp 448 3842 a(\(4.4\)) 448 4017 y @beginspecial @setspecial @endspecial(where) p Fn 711 4017 a(\026) p 791 4017 a(>) p Fp 887 4017 a(0) p 962 4017 a(is) p 1052 4017 a(tak) m(en) p 1299 4017 a(suc) m(h) p 1504 4017 a(that) p Fi 1700 3953 a(P) p Fm 1788 4040 a(j) p Fj(x) p Fm(j) p Fl(=1) p Fp 1961 4017 a(\() p Fn(e) p Fj 2038 3984 a(\026) p Fm(j) p Fj(x) p Fm(j) p Fh 2183 4017 a(\000) p Fp 2272 4017 a(1\)) p Fh 2378 4017 a(\024) p Fj 2484 3976 a(\021) p 2484 3996 38 4 v Fl 2485 4048 a(2) p Fp 2532 4017 a(.) p 2598 4017 a(By) p 2740 4017 a(\(4.4\)) p 2956 4017 a(and) p 3132 4017 a(the) p 3288 4017 a(fact) 448 4141 y(that) p Fn 645 4141 a(@) p Fl 693 4155 a(1) p Fn 733 4141 a(H) p Fj 809 4155 a(!) p Fh 884 4141 a(2) p 970 4141 a(A) p Fl 1043 4155 a(0) p Fp 1082 4141 a(,) p 1138 4141 a(w) m(e) p 1271 4141 a(ha) m(v) m(e) p Fh 997 4350 a(j) p Fn(e) p Fj 1064 4303 a(it) p Fm(L) p Ff 1162 4314 a(H) 1212 4331 y(!) r(;) p Fd(E) p Fp 1322 4350 a(\() p Fn(@) p Fl 1405 4364 a(1) p Fn 1445 4350 a(H) p Fj 1521 4364 a(!) p Fp 1571 4350 a(\)\() p Fn(!) p Fp 1716 4350 a(;) p Fn 1756 4350 a(x;) p 1848 4350 a(y) p Fp 1896 4350 a(\)) p Fh(j) p Fp 448 4350 a(\(4.5\)) 997 4500 y(=) p Fi 1093 4402 a(\014) 1093 4452 y(\014) 1093 4502 y(\014) 1120 4406 y(\020) p Fn 1170 4500 a(e) p Fj 1212 4462 a(itH) p Ff 1319 4470 a(!) p Fp 1369 4500 a(\() p Fn(@) p Fl 1452 4514 a(1) p Fn 1492 4500 a(H) p Fj 1568 4514 a(!) p Fp 1618 4500 a(\)) p Fn(e) p Fm 1695 4462 a(\000) p Fj(itH) p Ff 1857 4470 a(!) p Fi 1907 4406 a(\021) p Fp 1956 4500 a(\() p Fn(!) p Fp 2067 4500 a(;) p Fn 2107 4500 a(x;) p 2199 4500 a(y) p Fp 2247 4500 a(\)) p Fi 2282 4402 a(\014) 2282 4452 y(\014) 2282 4502 y(\014) p Fh 2336 4500 a(\024) p Fn 2432 4500 a(C) p Fj 2497 4514 a(t) p Fn 2526 4500 a(e) p Fm 2568 4462 a(\000) p Fj(\026) p Fd 2665 4439 a(0) p Fm 2688 4462 a(j) p Fj(x) p Fm(\000) p Fj(y) p Fm 2840 4462 a(j) p Fn 2863 4500 a(;) 448 4727 y @beginspecial @setspecial @endspecial Fp(for) p 592 4727 a(some) p 825 4727 a(constan) m(ts) p Fn 1233 4727 a(C) p Fj 1298 4741 a(t) p Fn 1361 4727 a(>) p Fp 1465 4727 a(0,) p Fn 1573 4727 a(\026) p Fm 1628 4694 a(0) p Fn 1684 4727 a(>) p Fp 1788 4727 a(0,) p 1896 4727 a(uniformly) p 2315 4727 a(in) p 2426 4727 a(\() p Fn(!) p Fp 2537 4727 a(;) p Fn 2577 4727 a(x;) p 2669 4727 a(y) p Fp 2717 4727 a(\)) p Fh 2786 4727 a(2) p Fp 2880 4727 a(\012) p Fh 2969 4727 a(\002) p Fk 3064 4727 a(Z) p 3084 4727 a(Z) p Fj 3138 4690 a(d) p Fh 3202 4727 a(\002) p Fk 3297 4727 a(Z) p 3317 4727 a(Z) p Fj 3371 4690 a(d) p Fp 3412 4727 a(.) p Fn 448 4852 a(C) p Fj 513 4866 a(t) p Fp 590 4852 a(is) p 699 4852 a(uniformly) p 1130 4852 a(b) s(ounded) p 1518 4852 a(w.r.t.) p Fn 1822 4852 a(t) p Fp(,) p 1931 4852 a(if) p Fh 2032 4852 a(j) p Fn(t) p Fh(j) p 2168 4852 a(\024) p Fn 2293 4852 a(T) p Fp 2406 4852 a(for) p 2562 4852 a(some) p Fn 2806 4852 a(T) p 2926 4852 a(>) p Fp 3050 4852 a(0.) p 3212 4852 a(Th) m(us,) 448 4976 y([) p Fn(x) p Fl 525 4990 a(1) p Fn 565 4976 a(;) p 605 4976 a(e) p Fj 647 4943 a(it) p Fm(L) p Ff 745 4954 a(H) 795 4962 y(!) p Fp 849 4976 a(\() p Fn(@) p Fl 932 4990 a(1) p Fn 972 4976 a(H) p Fj 1048 4990 a(!) p Fp 1098 4976 a(\)]) p Fh 1188 4976 a(2) p 1278 4976 a(A) p 1380 4976 a(\032) p 1481 4976 a(L) p Fl 1544 4943 a(2) p Fp 1583 4976 a(,) p 1642 4976 a(b) s(ecause) p 1981 4976 a([) p Fn(x) p Fl 2058 4990 a(1) p Fn 2097 4976 a(;) p Fp 2137 4976 a(\() p Fn(e) p Fj 2214 4943 a(it) p Fm(L) p Ff 2312 4954 a(H) 2362 4962 y(!) p Fp 2416 4976 a(\() p Fn(@) p Fl 2499 4990 a(1) p Fn 2539 4976 a(H) p Fj 2615 4990 a(!) p Fp 2665 4976 a(\)\)]\() p Fn(!) p Fp 2872 4976 a(;) p Fn 2912 4976 a(x;) p 3004 4976 a(y) p Fp 3052 4976 a(\)) p 3117 4976 a(=) p 3218 4976 a(\() p Fn(x) p Fl 3305 4990 a(1) p Fh 3366 4976 a(\000) p Fp 1897 5225 a(37) p eop %%Page: 38 38 38 37 bop Fn 448 573 a(y) p Fl 493 587 a(1) p Fp 532 573 a(\)\() p Fn(e) p Fj 644 540 a(it) p Fm(L) p Ff 742 551 a(H) 792 559 y(!) p Fp 846 573 a(\() p Fn(@) p Fl 929 587 a(1) p Fn 969 573 a(H) p Fj 1045 587 a(!) p Fp 1095 573 a(\)\)\() p Fn(!) p Fp 1276 573 a(;) p Fn 1316 573 a(x;) p 1408 573 a(y) p Fp 1456 573 a(\)) p 1525 573 a(deca) m(ys) p 1817 573 a(exp) s(onen) m(tially) p 2380 573 a(b) m(y) p 2509 573 a(\(4.5\).) p 2770 573 a(Hence) p Fn 3043 573 a(@) p Fl 3091 587 a(1) p Fn 3131 573 a(H) p Fj 3207 587 a(!) p Fp 3290 573 a(sat-) 448 697 y(is\014es) p 667 697 a(\(4.1\),) p 909 697 a(\(4.2\).) 589 822 y @beginspecial @setspecial @endspecial(\(2\)) p 744 822 a(Because) p 1099 822 a([) p Fn(x) p Fl 1176 836 a(1) p Fn 1216 822 a(;) p 1256 822 a(e) p Fj 1298 789 a(is) p Fm(L) p Ff 1404 800 a(H) 1454 808 y(!) p Fp 1507 822 a(\() p Fn(@) p Fl 1590 836 a(1) p Fn 1630 822 a(H) p Fj 1706 836 a(!) p Fp 1756 822 a(\)]) p Fh 1854 822 a(2) p 1953 822 a(A) p Fp(,) p 2091 822 a(and) p Fn 2275 822 a(H) p Fj 2351 836 a(!) p Fh 2440 822 a(2) p 2538 822 a(L) p Fl 2601 789 a(2) p Fp 2678 822 a(whic) m(h) p 2946 822 a(follo) m(ws) p 3253 822 a(from) 448 946 y(the) p 608 946 a(assumption) p 1092 946 a(that) p Fe 1292 946 a(E) p Fh(j) p Fn(V) p Fj 1439 960 a(!) p Fp 1489 946 a(\(0\)) p Fh(j) p Fl 1629 913 a(2) p Fn 1701 946 a(<) p Fh 1802 946 a(1) p Fp(,) p 1952 946 a(w) m(e) p 2089 946 a(ha) m(v) m(e) p Fh 2302 946 a(L) p Fj 2365 960 a(H) p Ff 2423 968 a(!) p Fp 2471 946 a([) p Fn(x) p Fl 2548 960 a(1) p Fn 2588 946 a(;) p 2628 946 a(e) p Fj 2670 913 a(is) p Fm(L) p Ff 2776 924 a(H) 2826 932 y(!) p Fp 2879 946 a(\() p Fn(@) p Fl 2962 960 a(1) p Fn 3002 946 a(H) p Fj 3078 960 a(!) p Fp 3128 946 a(\)]) p Fh 3219 946 a(2) p 3310 946 a(L) p Fl 3373 913 a(2) p Fp 3412 946 a(,) 448 1071 y(and) p 645 1071 a(therefore,) p 1077 1071 a([) p Fn(x) p Fl 1154 1085 a(1) p Fn 1194 1071 a(;) p 1234 1071 a(e) p Fj 1276 1038 a(is) p Fm(L) p Ff 1382 1049 a(H) 1432 1057 y(!) p Fp 1485 1071 a(\() p Fn(@) p Fl 1568 1085 a(1) p Fn 1608 1071 a(H) p Fj 1684 1085 a(!) p Fp 1734 1071 a(\)]) p Fh 1853 1071 a(2) p 1972 1071 a(D) p Fp 2045 1071 a(\() p Fh(L) p Fj 2143 1085 a(H) p Ff 2201 1093 a(!) p Fp 2250 1071 a(\).) p 2411 1071 a(By) p 2574 1071 a(\(4.4\),) p 2841 1071 a(\() p Fn(e) p Fj 2918 1038 a(itH) p Ff 3025 1046 a(!) p Fp 3075 1071 a(\)\() p Fn(!) p Fp 3221 1071 a(;) p Fn 3261 1071 a(x;) p 3353 1071 a(y) p Fp 3401 1071 a(\)) 448 1196 y(deca) m(ys) p 757 1196 a(exp) s(onen) m(tially) p 1339 1196 a(as) p 1471 1196 a(w) m(ell) p 1676 1196 a(as) p 1808 1196 a([) p Fn(x) p Fl 1885 1210 a(1) p Fn 1925 1196 a(;) p 1965 1196 a(e) p Fj 2007 1163 a(is) p Fm(L) p Ff 2113 1174 a(H) 2163 1182 y(!) p Fp 2215 1196 a(\() p Fn(@) p Fl 2298 1210 a(1) p Fn 2339 1196 a(H) p Fj 2415 1210 a(!) p Fp 2464 1196 a(\)]\() p Fn(!) p Fp 2635 1196 a(;) p Fn 2675 1196 a(x;) p 2767 1196 a(y) p Fp 2815 1196 a(\),) p 2933 1196 a(and) p 3130 1196 a(so) p 3262 1196 a(do) s(es) p Fi 448 1226 a(\020) p Fn 498 1320 a(e) p Fj 540 1287 a(it) p Fm(L) p Ff 638 1298 a(H) 688 1306 y(!) p Fp 741 1320 a([) p Fn(x) p Fl 818 1334 a(1) p Fn 858 1320 a(;) p 898 1320 a(e) p Fj 940 1287 a(is) p Fm(L) p Ff 1046 1298 a(H) 1096 1306 y(!) p Fp 1149 1320 a(\() p Fn(@) p Fl 1232 1334 a(1) p Fn 1272 1320 a(H) p Fj 1348 1334 a(!) p Fp 1398 1320 a(\)]) p Fi 1458 1226 a(\021) p Fp 1508 1320 a(\() p Fn(!) p Fp 1618 1320 a(;) p Fn 1658 1320 a(x;) p 1750 1320 a(y) p Fp 1798 1320 a(\).) p 1964 1320 a(Hence) p Fn 2256 1320 a(e) p Fj 2298 1287 a(it) p Fm(L) p Ff 2396 1298 a(H) 2446 1306 y(!) p Fi 2499 1226 a(\020) p Fp 2549 1320 a([) p Fn(x) p Fl 2626 1334 a(1) p Fn 2665 1320 a(;) p 2705 1320 a(e) p Fj 2747 1287 a(is) p Fm(L) p Ff 2853 1298 a(H) 2903 1306 y(!) p Fp 2956 1320 a(\() p Fn(@) p Fl 3039 1334 a(1) p Fn 3079 1320 a(H) p Fj 3155 1334 a(!) p Fp 3205 1320 a(\)]) p Fi 3265 1226 a(\021) p Fh 3377 1320 a(2) 448 1445 y(D) p Fp 521 1445 a(\() p Fn(@) p Fl 604 1459 a(1) p Fp 644 1445 a(\).) p 745 1381 60 4 v 745 1469 4 89 v 801 1469 V 745 1472 60 4 v 589 1660 a @beginspecial @setspecial @endspecial Fo(Pr) p 684 1660 a(o) p 725 1660 a(of) p 838 1660 a(of) p 949 1660 a(The) p 1097 1660 a(or) p 1176 1660 a(em) p 1331 1660 a(2) p Fp 1450 1660 a(By) p 1597 1660 a(the) p 1759 1660 a(same) p 1992 1660 a(argumen) m(t) p 2403 1660 a(as) p 2520 1660 a(in) p 2631 1660 a(the) p 2792 1660 a(pro) s(of) p 3035 1660 a(of) p 3143 1660 a(Lemma) 448 1785 y(3.2,) p 620 1785 a(w) m(e) p 754 1785 a(ha) m(v) m(e) p Fh 746 1995 a(T) p Fp 819 1995 a(\() p Fn(e) p Fj 896 1957 a(itH) p Ff 1003 1968 a(!) r(;) p Fd(E) p Fn 1109 1995 a(i) p Fp([) p Fn(H) p Fj 1241 2009 a(!) p Fn 1292 1995 a(;) p 1332 1995 a(x) p Fl 1384 2009 a(1) p Fp 1424 1995 a(]) p Fn(e) p Fm 1491 1957 a(\000) p Fj(itH) p Ff 1653 1968 a(!) r(;) p Fd(E) p Fn 1759 1995 a(P) p Fp 1830 1995 a(\)) p 1891 1995 a(=) p Fh 1987 1995 a(\000) p Fn(i) p 2114 1995 a(<) p 2210 1995 a(e) p Fj 2252 1947 a(it) p Fm(L) p Ff 2350 1958 a(H) 2400 1975 y(!) r(;) p Fd(E) p Fp 2510 1995 a(\() p Fn(@) p Fl 2593 2009 a(1) p Fn 2633 1995 a(H) p Fj 2709 2009 a(!) p Fp 2759 1995 a(\)) p Fn(;) p 2834 1995 a(P) p 2931 1995 a(>) p Fm 3002 2015 a(L) p Fc 3051 1996 a(2) p Fn 3114 1995 a(:) 448 2205 y @beginspecial @setspecial @endspecial Fp(By) p 591 2205 a(Lemma) p 915 2205 a(4.1,) p Fn 1087 2205 a(@) p Fl 1135 2219 a(1) p Fn 1175 2205 a(H) p Fj 1251 2219 a(!) p Fp 1331 2205 a(satis\014es) p 1666 2205 a(the) p 1823 2205 a(condition) p 2222 2205 a(to) p 2333 2205 a(use) p 2490 2205 a(Prop) s(osition) p 2979 2205 a(4.1.) p Fh 656 2416 a(\000) p Fn(i) p 783 2416 a() p Fm 1646 2435 a(L) p Fc 1695 2416 a(2) p Fp 1153 2565 a(=) p Fh 1249 2565 a(\000) p Fn(i) p 1377 2565 a(<) p 1473 2565 a(e) p Fj 1515 2527 a(it) p Fm(L) p Ff 1613 2538 a(H) 1663 2546 y(!) p Fp 1716 2565 a(\() p Fn(@) p Fl 1799 2579 a(1) p Fn 1839 2565 a(H) p Fj 1915 2579 a(!) p Fp 1965 2565 a(\)) p Fn(;) p 2040 2565 a(P) p 2137 2565 a(>) p Fm 2208 2585 a(L) p Fc 2257 2566 a(2) p Fp 1244 2750 a(+) p Fh(E) p Fi 1386 2636 a(Z) p Fj 1469 2662 a(t) p Fl 1432 2824 a(0) p Fn 1514 2750 a(ds) p 1655 2750 a(<) p 1751 2750 a(e) p Fj 1793 2703 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 2033 2714 a(H) 2083 2731 y(!) r(;) p Fd(E) p Fp 2193 2750 a([) p Fn(x) p Fl 2270 2764 a(1) p Fn 2309 2750 a(;) p 2349 2750 a(e) p Fj 2391 2713 a(is) p Fm(L) p Ff 2497 2724 a(H) 2547 2732 y(!) p Fp 2600 2750 a(\() p Fn(@) p Fl 2683 2764 a(1) p Fn 2723 2750 a(H) p Fj 2799 2764 a(!) p Fp 2849 2750 a(\)]) p Fn(;) p 2949 2750 a(P) p 3046 2750 a(>) p Fm 3117 2770 a(L) p Fc 3166 2751 a(2) p Fp 1153 2919 a(=:) p Fn 1275 2919 a(V) p Fp 1368 2919 a(+) p Fn 1459 2919 a(V) p 1532 2919 a(I) p 1579 2919 a(:) 448 3130 y @beginspecial @setspecial @endspecial Fp(By) p 591 3130 a(Prop) s(osition) p 1080 3130 a(2.2,) p 1252 3130 a(2.4,) p 1424 3130 a(and) p 1601 3130 a(2.8,) p Fn 1206 3340 a(V) p Fp 1304 3340 a(=) p Fh 1400 3340 a(\000) p Fn(i) p 1527 3340 a(<) p 1623 3340 a(e) p Fj 1665 3303 a(itH) p Ff 1772 3311 a(!) p Fp 1822 3340 a(\() p Fn(@) p Fl 1905 3354 a(1) p Fn 1945 3340 a(H) p Fj 2021 3354 a(!) p Fp 2071 3340 a(\)) p Fn(e) p Fm 2148 3303 a(\000) p Fj(itH) p Ff 2310 3311 a(!) p Fn 2360 3340 a(;) p 2400 3340 a(P) p 2497 3340 a(>) p Fm 2568 3360 a(L) p Fc 2617 3341 a(2) p Fp 1304 3490 a(=) p Fh 1400 3490 a(\000) p Fn(i) p Fh(T) p Fp 1575 3490 a(\() p Fn(e) p Fj 1652 3452 a(itH) p Ff 1759 3460 a(!) p Fp 1809 3490 a(\() p Fn(@) p Fl 1892 3504 a(1) p Fn 1932 3490 a(H) p Fj 2008 3504 a(!) p Fp 2058 3490 a(\)) p Fn(e) p Fm 2135 3452 a(\000) p Fj(itH) p Ff 2297 3460 a(!) p Fn 2347 3490 a(P) p Fp 2418 3490 a(\)) 1304 3639 y(=) p Fh 1400 3639 a(\000) p Fn(i) p Fh(T) p Fp 1575 3639 a(\(\() p Fn(@) p Fl 1693 3653 a(1) p Fn 1733 3639 a(H) p Fj 1809 3653 a(!) p Fp 1859 3639 a(\)) p Fn(P) p Fp 1965 3639 a(\)) 1304 3788 y(=) p 1400 3788 a(0) p Fn(:) 448 3999 y @beginspecial @setspecial @endspecial Fp(Therefore,) 976 4169 y(1) p 970 4210 57 4 v Fh 970 4293 a(E) 1037 4231 y(T) p Fp 1109 4231 a(\() p Fn(e) p Fj 1186 4193 a(itH) p Ff 1293 4204 a(!) r(;) p Fd(E) p Fn 1400 4231 a(i) p Fp([) p Fn(H) p Fj 1532 4245 a(!) p Fn 1582 4231 a(;) p 1622 4231 a(x) p Fl 1674 4245 a(1) p Fp 1714 4231 a(]) p Fn(e) p Fm 1781 4193 a(\000) p Fj(itH) p Ff 1943 4204 a(!) r(;) p Fd(E) p Fn 2049 4231 a(P) p Fp 2120 4231 a(\)) 960 4456 y(=) p Fi 1056 4341 a(Z) p Fj 1139 4367 a(t) p Fl 1103 4529 a(0) p Fn 1184 4456 a(ds) p 1325 4456 a(<) p 1421 4456 a(e) p Fj 1463 4408 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 1703 4419 a(H) 1753 4436 y(!) r(;) p Fd(E) p Fp 1863 4456 a([) p Fn(x) p Fl 1940 4470 a(1) p Fn 1979 4456 a(;) p 2019 4456 a(e) p Fj 2061 4418 a(is) p Fm(L) p Ff 2167 4429 a(H) 2217 4437 y(!) p Fp 2270 4456 a(\() p Fn(@) p Fl 2353 4470 a(1) p Fn 2393 4456 a(H) p Fj 2469 4470 a(!) p Fp 2519 4456 a(\)]) p Fn(;) p 2619 4456 a(P) p 2716 4456 a(>) p Fm 2787 4476 a(L) p Fc 2836 4457 a(2) p Fn 2900 4456 a(:) 448 4702 y @beginspecial @setspecial @endspecial Fp(By) p 591 4702 a(Lemma) p 915 4702 a(4.1,) p 1087 4702 a(w) m(e) p 1221 4702 a(can) p 1388 4702 a(use) p 1545 4702 a(Prop) s(osition) p 2034 4702 a(4.1) p 2181 4702 a(for) p 2320 4702 a([) p Fn(x) p Fl 2397 4716 a(1) p Fn 2436 4702 a(;) p 2476 4702 a(e) p Fj 2518 4669 a(is) p Fm(L) p Ff 2624 4680 a(H) 2674 4688 y(!) p Fp 2727 4702 a(\() p Fn(@) p Fl 2810 4716 a(1) p Fn 2850 4702 a(H) p Fj 2926 4716 a(!) p Fp 2976 4702 a(\)].) p Fi 462 4833 a(Z) p Fj 545 4860 a(t) p Fl 508 5022 a(0) p Fn 590 4948 a(ds) p 730 4948 a(<) p 826 4948 a(e) p Fj 868 4901 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 1108 4912 a(H) 1158 4929 y(!) r(;) p Fd(E) p Fp 1268 4948 a([) p Fn(x) p Fl 1345 4962 a(1) p Fn 1385 4948 a(;) p 1425 4948 a(e) p Fj 1467 4911 a(is) p Fm(L) p Ff 1573 4922 a(H) 1623 4930 y(!) p Fp 1676 4948 a(\() p Fn(@) p Fl 1759 4962 a(1) p Fn 1799 4948 a(H) p Fj 1875 4962 a(!) p Fp 1925 4948 a(\)]) p Fn(;) p 2025 4948 a(P) p 2122 4948 a(>) p Fm 2193 4968 a(L) p Fc 2242 4949 a(2) p Fp 1897 5225 a(38) p eop %%Page: 39 39 39 38 bop Fp 462 611 a(=) p Fi 558 496 a(Z) p Fj 641 522 a(t) p Fl 604 685 a(0) p Fn 686 611 a(ds) p 826 611 a(<) p 922 611 a(e) p Fj 964 574 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 1204 585 a(H) 1254 593 y(!) p Fp 1308 611 a([) p Fn(x) p Fl 1385 625 a(1) p Fn 1424 611 a(;) p 1464 611 a(e) p Fj 1506 574 a(is) p Fm(L) p Ff 1612 585 a(H) 1662 593 y(!) p Fp 1715 611 a(\() p Fn(@) p Fl 1798 625 a(1) p Fn 1838 611 a(H) p Fj 1914 625 a(!) p Fp 1964 611 a(\)]) p Fn(;) p 2064 611 a(P) p 2162 611 a(>) p Fm 2233 631 a(L) p Fc 2282 612 a(2) p Fp 462 847 a(+) p Fn(i) p Fh(E) p Fi 635 733 a(Z) p Fj 718 759 a(t) p Fl 681 921 a(0) p Fn 763 847 a(ds) p Fi 893 733 a(Z) p Fj 976 759 a(t) p Fm(\000) p Fj(s) p Fl 940 921 a(0) p Fn 1109 847 a(du) p 1259 847 a(<) p 1355 847 a(e) p Fj 1397 800 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fm(\000) p Fj(u) p Fl(\)) p Fm(L) p Ff 1733 811 a(H) 1783 828 y(!) r(;) p Fd(E) p Fi 1892 753 a(h) p Fn 1932 847 a(x) p Fl 1984 861 a(1) p Fn 2023 847 a(;) p 2063 847 a(e) p Fj 2105 810 a(iu) p Fm(L) p Ff 2219 821 a(H) 2269 829 y(!) p Fp 2322 847 a([) p Fn(x) p Fl 2399 861 a(1) p Fn 2439 847 a(;) p 2479 847 a(e) p Fj 2521 810 a(is) p Fm(L) p Ff 2627 821 a(H) 2677 829 y(!) p Fp 2729 847 a(\() p Fn(@) p Fl 2812 861 a(1) p Fn 2853 847 a(H) p Fj 2929 861 a(!) p Fp 2978 847 a(\)]) p Fi 3038 753 a(i) p Fn 3078 847 a(;) p 3118 847 a(P) p 3215 847 a(>) p Fm 3286 867 a(L) p Fc 3335 848 a(2) p Fn 3398 847 a(:) 448 1092 y @beginspecial @setspecial @endspecial Fp(By) p 589 1092 a(\(4.4\),) p Fi 829 998 a(h) p Fn 869 1092 a(x) p Fl 921 1106 a(1) p Fn 960 1092 a(;) p 1000 1092 a(e) p Fj 1042 1059 a(iuH) p Ff 1165 1070 a(!) r(;) p Fd(E) p Fp 1271 1092 a([) p Fn(x) p Fl 1348 1106 a(1) p Fn 1388 1092 a(;) p 1428 1092 a(e) p Fj 1470 1059 a(isH) p Ff 1585 1070 a(!) r(;) p Fd(E) p Fp 1690 1092 a(\() p Fn(@) p Fl 1773 1106 a(1) p Fn 1813 1092 a(H) p Fj 1889 1106 a(!) p Fp 1939 1092 a(\)]) p Fi 1999 998 a(i) p Fp 2067 1092 a(is) p 2156 1092 a(uniformly) p 2569 1092 a(b) s(ounded) p 2938 1092 a(in) p Fh 3041 1092 a(L) p Fl 3104 1059 a(2) p Fp 3172 1092 a(for) p Fn 3309 1092 a(s) p Fh 3377 1092 a(2) p Fp 448 1217 a([0) p Fn(;) p 558 1217 a(t) p Fp(],) p Fn 673 1217 a(u) p Fh 751 1217 a(2) p Fp 837 1217 a([0) p Fn(;) p 947 1217 a(t) p Fp(].) p 1073 1217 a(Therefore,) p 1511 1217 a(for) p 1650 1217 a(\014xed) p Fn 1870 1217 a(t) p Fp(,) p 1959 1217 a(the) p 2115 1217 a(second) p 2409 1217 a(term) p 2627 1217 a(of) p 2731 1217 a(RHS) p 2947 1217 a(in) p 3053 1217 a(the) p 3210 1217 a(ab) s(o) m(v) m(e) 448 1341 y(expression) p 887 1341 a(go) s(es) p 1088 1341 a(to) p 1200 1341 a(zero) p 1393 1341 a(as) p Fh 1505 1341 a(E) p 1588 1341 a(#) p Fp 1660 1341 a(0.) p 1774 1341 a(Then,) p 2038 1341 a(w) m(e) p 2172 1341 a(compute,) p 2567 1341 a(b) m(y) p 2694 1341 a(using) p 2933 1341 a(the) p 3090 1341 a(fact) p 3270 1341 a(that) p Fn 448 1466 a(e) p Fj 490 1433 a(it) p Fm(L) p Ff 588 1444 a(H) 638 1452 y(!) p Fn 692 1466 a(P) p Fp 788 1466 a(=) p Fn 884 1466 a(P) p Fp 955 1466 a(,) p 1010 1466 a(and) p Fn 1187 1466 a(P) p Fh 1283 1466 a(2) p 1369 1466 a(D) p Fp 1442 1466 a(\() p Fn(@) p Fl 1525 1480 a(1) p Fp 1565 1466 a(\),) 809 1692 y(lim) p Fm 815 1752 a(E) p 858 1752 a(#) p Fl(0) p Fi 951 1577 a(Z) p Fj 1034 1603 a(t) p Fl 997 1765 a(0) p Fn 1078 1692 a(ds) p 1194 1692 a(<) p 1289 1692 a(e) p Fj 1331 1644 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 1571 1655 a(H) 1621 1672 y(!) r(;) p Fd(E) p Fp 1732 1692 a([) p Fn(x) p Fl 1809 1706 a(1) p Fn 1848 1692 a(;) p 1888 1692 a(e) p Fj 1930 1654 a(is) p Fm(L) p Ff 2036 1665 a(H) 2086 1673 y(!) p Fp 2139 1692 a(\() p Fn(@) p Fl 2222 1706 a(1) p Fn 2262 1692 a(H) p Fj 2338 1706 a(!) p Fp 2388 1692 a(\)]) p Fn(;) p 2488 1692 a(P) p 2585 1692 a(>) p Fm 2656 1711 a(L) p Fc 2705 1692 a(2) p Fp 1194 1936 a(=) p Fi 1289 1821 a(Z) p Fj 1373 1847 a(t) p Fl 1336 2009 a(0) p Fn 1417 1936 a(ds) p 1558 1936 a(<) p 1654 1936 a(e) p Fj 1696 1898 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 1936 1909 a(H) 1986 1917 y(!) p Fp 2039 1936 a([) p Fn(x) p Fl 2116 1950 a(1) p Fn 2156 1936 a(;) p 2196 1936 a(e) p Fj 2238 1898 a(is) p Fm(L) p Ff 2344 1909 a(H) 2394 1917 y(!) p Fp 2447 1936 a(\() p Fn(@) p Fl 2530 1950 a(1) p Fn 2570 1936 a(H) p Fj 2646 1950 a(!) p Fp 2696 1936 a(\)]) p Fn(;) p 2796 1936 a(P) p 2893 1936 a(>) p Fm 2964 1955 a(L) p Fc 3013 1936 a(2) p Fp 1194 2172 a(=) p Fi 1289 2057 a(Z) p Fj 1373 2083 a(t) p Fl 1336 2246 a(0) p Fn 1417 2172 a(ds) p 1558 2172 a(<) p Fp 1654 2172 a([) p Fn(x) p Fl 1731 2186 a(1) p Fn 1770 2172 a(;) p 1810 2172 a(e) p Fj 1852 2134 a(is) p Fm(L) p Ff 1958 2145 a(H) 2008 2153 y(!) p Fp 2061 2172 a(\() p Fn(@) p Fl 2144 2186 a(1) p Fn 2184 2172 a(H) p Fj 2260 2186 a(!) p Fp 2310 2172 a(\)]) p Fn(;) p 2410 2172 a(P) p 2507 2172 a(>) p Fm 2578 2192 a(L) p Fc 2627 2173 a(2) p Fp 1194 2408 a(=) p Fi 1289 2293 a(Z) p Fj 1373 2320 a(t) p Fl 1336 2482 a(0) p Fn 1417 2408 a(ds) p 1558 2408 a(<) p 1654 2408 a(e) p Fj 1696 2371 a(is) p Fm(L) p Ff 1802 2382 a(H) 1852 2390 y(!) p Fp 1904 2408 a(\() p Fn(@) p Fl 1987 2422 a(1) p Fn 2027 2408 a(H) p Fj 2103 2422 a(!) p Fp 2153 2408 a(\)) p Fn(;) p 2228 2408 a(@) p Fl 2276 2422 a(1) p Fn 2317 2408 a(P) p 2413 2408 a(>) p Fm 2484 2428 a(L) p Fc 2533 2409 a(2) p Fn 2596 2408 a(:) 448 2619 y @beginspecial @setspecial @endspecial Fp(W) p 533 2619 a(e) p 605 2619 a(pro) s(ceed) p 941 2619 a(as) p 1053 2619 a(in) p 1159 2619 a(the) p 1315 2619 a(pro) s(of) p 1553 2619 a(of) p 1656 2619 a(Theorem) p 2040 2619 a(1,) p 2142 2619 a(using) p 2379 2619 a(Lemma) p 2704 2619 a(3.4,) p 2876 2619 a(3.8,) p Fi 637 2725 a(Z) p Fj 720 2751 a(t) p Fl 683 2913 a(0) p Fn 765 2840 a(ds) p 905 2840 a(<) p 1001 2840 a(e) p Fj 1043 2802 a(is) p Fm(L) p Ff 1149 2813 a(H) 1199 2821 y(!) p Fp 1252 2840 a(\() p Fn(@) p Fl 1335 2854 a(1) p Fn 1375 2840 a(H) p Fj 1451 2854 a(!) p Fp 1501 2840 a(\)) p Fn(;) p 1576 2840 a(@) p Fl 1624 2854 a(1) p Fn 1664 2840 a(P) p 1760 2840 a(>) p Fm 1831 2859 a(L) p Fc 1880 2840 a(2) p Fp 637 3076 a(=) p Fi 733 2961 a(Z) p Fj 816 2987 a(t) p Fl 779 3150 a(0) p Fn 861 3076 a(ds) p 1001 3076 a(<) p 1097 3076 a(e) p Fj 1139 3038 a(is) p Fm(L) p Ff 1245 3049 a(H) 1295 3057 y(!) p Fh 1348 3076 a(L) p Fj 1411 3090 a(H) p Ff 1469 3098 a(!) p Fi 1517 2982 a(\020h) p Fp 1606 3076 a([) p Fn(x) p Fl 1683 3090 a(1) p Fn 1723 3076 a(;) p 1763 3076 a(P) p Fp 1834 3076 a(]) p Fn(;) p 1899 3076 a(P) p Fi 1970 2982 a(i) q(\021) p Fn 2059 3076 a(;) p 2099 3076 a(@) p Fl 2147 3090 a(1) p Fn 2188 3076 a(P) p 2284 3076 a(>) p Fm 2355 3096 a(L) p Fc 2404 3077 a(2) p Fp 637 3312 a(=) p Fh 733 3312 a(\000) p Fn(i) p Fi 850 3197 a(Z) p Fj 933 3224 a(t) p Fl 896 3386 a(0) p Fn 978 3312 a(ds) 1124 3251 y(d) p 1103 3291 90 4 v 1103 3375 a(ds) 1228 3312 y(<) p 1324 3312 a(e) p Fj 1366 3275 a(is) p Fm(L) p Ff 1472 3286 a(H) 1522 3294 y(!) p Fi 1575 3218 a(\020) o(h) p Fp 1663 3312 a([) p Fn(x) p Fl 1740 3326 a(1) p Fn 1780 3312 a(;) p 1820 3312 a(P) p Fp 1891 3312 a(]) p Fn(;) p 1956 3312 a(P) p Fi 2027 3218 a(i) q(\021) p Fn 2117 3312 a(;) p 2157 3312 a(@) p Fl 2205 3326 a(1) p Fn 2245 3312 a(P) p 2341 3312 a(>) p Fm 2412 3332 a(L) p Fc 2461 3313 a(2) p Fp 637 3517 a(=) p Fh 733 3517 a(\000) p Fn(i) p 860 3517 a(<) p 956 3517 a(e) p Fj 998 3479 a(it) p Fm(L) p Ff 1096 3490 a(H) 1146 3498 y(!) p Fi 1199 3423 a(\020h) p Fp 1288 3517 a([) p Fn(x) p Fl 1365 3531 a(1) p Fn 1405 3517 a(;) p 1445 3517 a(P) p Fp 1516 3517 a(]) p Fn(;) p 1581 3517 a(P) p Fi 1652 3423 a(i) q(\021) p Fn 1742 3517 a(;) p 1782 3517 a(@) p Fl 1830 3531 a(1) p Fn 1870 3517 a(P) p 1966 3517 a(>) p Fm 2037 3536 a(L) p Fc 2086 3517 a(2) p Fp 2149 3517 a(+) p Fn(i) p 2277 3517 a(<) p Fi 2373 3423 a(h) p Fp 2412 3517 a([) p Fn(x) p Fl 2489 3531 a(1) p Fn 2528 3517 a(;) p 2568 3517 a(P) p Fp 2639 3517 a(]) p Fn(;) p 2704 3517 a(P) p Fi 2775 3423 a(i) p Fn 2816 3517 a(;) p 2856 3517 a(@) p Fl 2904 3531 a(1) p Fn 2944 3517 a(P) p 3040 3517 a(>) p Fm 3111 3536 a(L) p Fc 3160 3517 a(2) p Fn 3223 3517 a(:) 448 3706 y @beginspecial @setspecial @endspecial Fp(The) p 634 3706 a(second) p 926 3706 a(term) p 1142 3706 a(in) p 1247 3706 a(the) p 1402 3706 a(ab) s(o) m(v) m(e) p 1659 3706 a(expression) p 2095 3706 a(v) p 2138 3706 a(anishes) p 2451 3706 a(as) p 2561 3706 a(w) m(e) p 2694 3706 a(sa) m(w) p 2867 3706 a(in) p 2972 3706 a(the) p 3128 3706 a(pro) s(of) p 3364 3706 a(of) 448 3831 y(Theorem) p 832 3831 a(1.) p 944 3831 a(On) p 1095 3831 a(the) p 1252 3831 a(other) p 1489 3831 a(hand,) p 1742 3831 a(b) m(y) p 1868 3831 a(sp) s(ectral) p 2210 3831 a(theorem,) 1494 3995 y(1) p 1484 4035 66 4 v Fn 1484 4119 a(T) p Fi 1575 3941 a(Z) p Fj 1658 3968 a(T) p Fl 1621 4130 a(0) p Fn 1728 4056 a(dt) p 1833 4056 a(e) p Fj 1875 4019 a(it) p Fm(L) p Ff 1973 4030 a(H) 2023 4038 y(!) p Fh 2102 4056 a(!) p Fn 2218 4056 a(P) p Fm 2276 4075 a(f) p Fl(0) p Fm(g) p Fn 2386 4056 a(;) 448 4279 y @beginspecial @setspecial @endspecial Fp(strongly) p 802 4279 a(in) p Fh 910 4279 a(L) p Fl 973 4246 a(2) p Fp 1045 4279 a(as) p Fn 1158 4279 a(T) p Fh 1253 4279 a(") p 1327 4279 a(1) p Fp(,) p 1475 4279 a(where) p Fn 1740 4279 a(P) p Fm 1798 4298 a(f) p Fl(0) p Fm(g) p Fp 1941 4279 a(is) p 2034 4279 a(the) p 2193 4279 a(orthogonal) p 2650 4279 a(pro) p 2787 4279 a(jection) p 3084 4279 a(on) m(to) p 3290 4279 a(Ker) 448 4404 y(\() p Fh(L) p Fj 546 4418 a(H) p Ff 604 4426 a(!) p Fp 653 4404 a(\).) p 754 4404 a(Th) m(us,) p 1010 4404 a(b) m(y) p 1136 4404 a(Lemma) p 1461 4404 a(3.10,) 964 4634 y(lim) p Fj 949 4694 a(T) p Fm 1000 4694 a("1) p Fp 1141 4573 a(1) p 1131 4613 V Fn 1131 4697 a(T) p Fi 1222 4519 a(Z) p Fj 1305 4546 a(T) p Fl 1268 4708 a(0) p Fn 1400 4634 a(dt) p 1506 4634 a(<) p 1602 4634 a(e) p Fj 1644 4597 a(it) p Fm(L) p Ff 1742 4608 a(H) 1792 4616 y(!) p Fi 1845 4540 a(\020h) p Fp 1934 4634 a([) p Fn(x) p Fl 2011 4648 a(1) p Fn 2050 4634 a(;) p 2090 4634 a(P) p Fp 2161 4634 a(]) p Fn(;) p 2226 4634 a(P) p Fi 2297 4540 a(i) r(\021) p Fn 2387 4634 a(;) p 2427 4634 a(@) p Fl 2475 4648 a(1) p Fn 2515 4634 a(P) p 2612 4634 a(>) p Fm 2683 4654 a(L) p Fc 2732 4635 a(2) p Fp 2770 4634 a(=) p 2866 4634 a(0) p Fn(;) 448 4857 y @beginspecial @setspecial @endspecial Fp(and) p 625 4857 a(w) m(e) p 759 4857 a(pro) m(v) m(e) p Fn 1004 4857 a(\033) p Fl 1056 4871 a(1) p Fp 1096 4857 a(\() p Fn(!) s(;) p 1231 4857 a(\017) p Fj 1268 4871 a(F) p Fp 1327 4857 a(\)) p 1387 4857 a(=) p 1483 4857 a(0,) p 1584 4857 a(for) p 1723 4857 a(a.e.) p Fn 1900 4857 a(!) p Fp 1960 4857 a(.) p 2026 4793 60 4 v 2026 4882 4 89 v 2081 4882 V 2026 4885 60 4 v 1897 5225 a(39) p eop %%Page: 40 40 40 39 bop Fe 448 573 a(Remark) p 846 573 a(4.1) p 1025 573 a @beginspecial @setspecial @endspecial Fo(If) p Fn 1122 573 a(\025) p Fo 1209 573 a(is) p 1308 573 a(su\016ciently) p 1768 573 a(lar) p 1870 573 a(ge,) p 2017 573 a(we) p 2153 573 a(have) p 2364 573 a(the) p 2517 573 a(fol) p 2619 573 a(lowing) p 2904 573 a(dynamic) p 3230 573 a(al) p 3335 573 a(lo-) 448 697 y(c) p 485 697 a(alization) p 855 697 a(estimate) p Fe 1354 910 a(E) p Fh(j) p Fn(e) p Fj 1490 873 a(itH) p Ff 1597 881 a(!) p Fp 1647 910 a(\() p Fn(!) p Fp 1757 910 a(;) p Fn 1797 910 a(x;) p 1889 910 a(y) p Fp 1937 910 a(\)) p Fh(j) p 2024 910 a(\024) p Fn 2120 910 a(C) p 2192 910 a(e) p Fm 2234 873 a(\000) p Fj(\026) p Fm(j) p Fj(x) p Fm(\000) p Fj(y) p Fm 2483 873 a(j) p Fn 2506 910 a(;) p Fp 448 910 a(\(4.6\)) 448 1123 y @beginspecial @setspecial @endspecial Fo(for) p 600 1123 a(some) p 839 1123 a(c) p 876 1123 a(onstants) p Fn 1246 1123 a(C) p 1355 1123 a(>) p Fp 1463 1123 a(0) p Fo(,) p Fn 1578 1123 a(\026) p 1670 1123 a(>) p Fp 1778 1123 a(0) p Fo(,) p 1893 1123 a(indep) p 2101 1123 a(endent) p 2404 1123 a(of) p Fn 2517 1123 a(t) p Fh 2588 1123 a(2) p Fp 2686 1123 a(I) p 2704 1123 a(R) p Fo(,) p Fn 2839 1123 a(x) p Fo(,) p Fn 2960 1123 a(y) p Fh 3046 1123 a(2) p Fk 3144 1123 a(Z) p 3163 1123 a(Z) p Fj 3218 1087 a(d) p Fo 3298 1123 a(\([1,) 448 1248 y(2) q(,) p 562 1248 a(4]\).) p 764 1248 a(In) p 889 1248 a(this) p 1070 1248 a(c) p 1107 1248 a(ase,) p 1302 1248 a(op) p 1389 1248 a(er) p 1464 1248 a(ations) p Fp 1744 1248 a(lim) p Fm 1870 1263 a(E) p 1913 1263 a(#) p Fl(0) p Fo 2027 1248 a(and) p Fi 2211 1179 a(R) p Fm 2266 1205 a(1) p Fl 2250 1275 a(0) p Fn 2356 1248 a(dt) p 2473 1248 a(e) p Fm 2515 1215 a(\000) p Fj(\016) r(t) p Fo 2673 1248 a(in) p 2792 1248 a(the) p 2949 1248 a(de\014nition) p 3363 1248 a(of) p Fn 448 1372 a(\033) p Fl 500 1386 a(2) p Fp 540 1372 a(\() p Fn(!) s(;) p 675 1372 a(\017) p Fj 712 1386 a(F) p Fp 771 1372 a(\)) p Fo 839 1372 a(c) p 876 1372 a(an) p 1006 1372 a(b) p 1043 1372 a(e) p 1117 1372 a(exchange) p 1465 1372 a(d.) p 1582 1372 a(In) p 1701 1372 a(fact,) p 1908 1372 a(we) p 2043 1372 a(c) p 2080 1372 a(an) p 2210 1372 a(show) p Fp 1199 1550 a(1) p 1194 1591 57 4 v Fh 1194 1674 a(E) 1260 1612 y(T) p Fp 1333 1612 a(\() p Fn(e) p Fj 1410 1574 a(itH) p Ff 1517 1585 a(!) r(;) p Fd(E) p Fn 1623 1612 a(i) p Fp([) p Fn(H) p Fj 1755 1626 a(!) p Fn 1806 1612 a(;) p 1846 1612 a(x) p Fl 1898 1626 a(1) p Fp 1938 1612 a(]) p Fn(e) p Fm 2005 1574 a(\000) p Fj(itH) p Ff 2167 1585 a(!) r(;) p Fd(E) p Fn 2273 1612 a(P) p Fp 2344 1612 a(\)) p 2405 1612 a(=) p Fn 2501 1612 a(O) p Fp 2573 1612 a(\() p Fn(t) p Fp(\)) p Fn(;) p Fp 448 1612 a(\(4.7\)) 448 1839 y @beginspecial @setspecial @endspecial Fo(as) p Fn 564 1839 a(t) p Fh 623 1839 a(") p 693 1839 a(1) p Fo(,) p 845 1839 a(uniformly) p 1259 1839 a(in) p Fh 1371 1839 a(E) p Fo 1427 1839 a(.) p 1497 1839 a(T) p 1555 1839 a(o) p 1634 1839 a(show) p 1857 1839 a(\(4.7\),) p 2112 1839 a(we) p 2247 1839 a(use) p 2407 1839 a(Pr) p 2502 1839 a(op) p 2589 1839 a(osition) p 2891 1839 a(4.1,) p Fp 976 2017 a(1) p 970 2058 V Fh 970 2141 a(E) 1037 2079 y(T) p Fp 1109 2079 a(\() p Fn(e) p Fj 1186 2041 a(itH) p Ff 1293 2052 a(!) r(;) p Fd(E) p Fn 1400 2079 a(i) p Fp([) p Fn(H) p Fj 1532 2093 a(!) p Fn 1582 2079 a(;) p 1622 2079 a(x) p Fl 1674 2093 a(1) p Fp 1714 2079 a(]) p Fn(e) p Fm 1781 2041 a(\000) p Fj(itH) p Ff 1943 2052 a(!) r(;) p Fd(E) p Fn 2049 2079 a(P) p Fp 2120 2079 a(\)) 960 2304 y(=) p Fi 1056 2189 a(Z) p Fj 1139 2215 a(t) p Fl 1103 2378 a(0) p Fn 1184 2304 a(ds) p 1325 2304 a(<) p 1421 2304 a(e) p Fj 1463 2256 a(i) p Fl(\() p Fj(t) p Fm(\000) p Fj(s) p Fl(\)) p Fm(L) p Ff 1703 2267 a(H) 1753 2284 y(!) r(;) p Fd(E) p Fp 1863 2304 a([) p Fn(x) p Fl 1940 2318 a(1) p Fn 1979 2304 a(;) p 2019 2304 a(e) p Fj 2061 2266 a(is) p Fm(L) p Ff 2167 2277 a(H) 2217 2285 y(!) p Fp 2270 2304 a(\() p Fn(@) p Fl 2353 2318 a(1) p Fn 2393 2304 a(H) p Fj 2469 2318 a(!) p Fp 2519 2304 a(\)]) p Fn(;) p 2619 2304 a(P) p 2716 2304 a(>) p Fm 2787 2324 a(L) p Fc 2836 2305 a(2) p Fn 2900 2304 a(:) 448 2553 y @beginspecial @setspecial @endspecial Fo(\(4.6\)) p 676 2553 a(implies) p 987 2553 a(that) p Fp 1173 2553 a([) p Fn(x) p Fl 1250 2567 a(1) p Fn 1290 2553 a(;) p 1330 2553 a(e) p Fj 1372 2520 a(is) p Fm(L) p Ff 1478 2531 a(H) 1528 2539 y(!) p Fp 1581 2553 a(\() p Fn(@) p Fl 1664 2567 a(1) p Fn 1704 2553 a(H) p Fj 1780 2567 a(!) p Fp 1830 2553 a(\)]) p Fo 1923 2553 a(is) p 2020 2553 a(uniformly) p 2435 2553 a(b) p 2472 2553 a(ounde) p 2701 2553 a(d) p 2781 2553 a(in) p Fh 2893 2553 a(L) p Fl 2956 2520 a(2) p Fo 2995 2553 a(.) p 3065 2553 a(In) p 3183 2553 a(fact,) p Fh 704 2766 a(j) p Fn(e) p Fj 771 2728 a(is) p Fm(L) p Ff 877 2739 a(H) 927 2747 y(!) p Fp 979 2766 a(\() p Fn(@) p Fl 1062 2780 a(1) p Fn 1102 2766 a(H) p Fj 1178 2780 a(!) p Fp 1228 2766 a(\)\() p Fn(!) p Fp 1374 2766 a(;) p Fn 1414 2766 a(x;) p 1506 2766 a(y) p Fp 1554 2766 a(\)) p Fh(j) p Fl 1614 2728 a(2) p Fp 448 2766 a(\(4.8\)) p Fh 704 2915 a(\024) p Fp 799 2915 a(2) p Fn(d) p Fh(j) p Fn(e) p Fj 958 2878 a(is) p Fm(L) p Ff 1064 2889 a(H) 1114 2897 y(!) p Fp 1168 2915 a(\() p Fn(@) p Fl 1251 2929 a(1) p Fn 1291 2915 a(H) p Fj 1367 2929 a(!) p Fp 1417 2915 a(\)\() p Fn(!) p Fp 1563 2915 a(;) p Fn 1603 2915 a(x;) p 1695 2915 a(y) p Fp 1743 2915 a(\)) p Fh(j) 704 3065 y(\024) p Fp 799 3065 a(2) p Fn(d) p Fi 995 2984 a(X) p Fj 907 3182 a(z) p Fc 940 3191 a(1) p Fj 975 3182 a(;z) p Fc 1028 3191 a(2) p Fm 1062 3182 a(2) p Fg(Z) p 1124 3182 a(Z) p Ff 1167 3157 a(d) p Fh 1219 3065 a(j) p Fn(e) p Fj 1286 3027 a(isH) p Ff 1401 3035 a(!) p Fp 1450 3065 a(\() p Fn(!) p Fp 1560 3065 a(;) p Fn 1600 3065 a(x;) p 1692 3065 a(z) p Fl 1734 3079 a(1) p Fp 1775 3065 a(\)) p Fh(jj) p Fn(@) p Fl 1908 3079 a(1) p Fn 1948 3065 a(H) p Fj 2024 3079 a(!) p Fp 2074 3065 a(\() p Fn(!) p Fp 2184 3065 a(;) p Fn 2224 3065 a(z) p Fl 2266 3079 a(1) p Fn 2307 3065 a(;) p 2347 3065 a(z) p Fl 2389 3079 a(2) p Fp 2429 3065 a(\)) p Fh(jj) p Fn(e) p Fm 2556 3027 a(\000) p Fj(isH) p Ff 2726 3035 a(!) p Fp 2775 3065 a(\() p Fn(!) p Fp 2886 3065 a(;) p Fn 2926 3065 a(z) p Fl 2968 3079 a(2) p Fn 3008 3065 a(;) p 3048 3065 a(y) p Fp 3096 3065 a(\)) p Fh(j) p Fn(:) 448 3368 y @beginspecial @setspecial @endspecial Fo(We) p 615 3368 a(use) p 738 3368 a(d) p Fh 818 3368 a(j) p Fp(\() p Fn(@) p Fl 926 3382 a(1) p Fn 966 3368 a(H) p Fj 1042 3382 a(!) p Fp 1092 3368 a(\)\() p Fn(!) p Fp 1238 3368 a(;) p Fn 1278 3368 a(x;) p 1370 3368 a(y) p Fp 1418 3368 a(\)) p Fh(j) p 1506 3368 a(\024) p 1604 3368 a(k) p Fn(@) p Fl 1697 3382 a(1) p Fn 1737 3368 a(H) p Fj 1813 3382 a(!) p Fh 1863 3368 a(k) p Fj 1908 3382 a(op) p Fh 2009 3368 a(\024) p Fp 2107 3368 a(2) p Fn(d) p Fo(.) p 2273 3368 a(We) p 2439 3368 a(take) p 2633 3368 a(exp) p 2758 3368 a(e) p 2795 3368 a(ctation,) p 3132 3368 a(and) p 3309 3368 a(use) 448 3493 y(Schwarz) p 803 3493 a(ine) p 919 3493 a(quality) p 1214 3493 a(w.r.t.) p Fe 1468 3493 a(E) p Fo(.) p Fe 824 3706 a(E) p Fp(\() p Fo(RHS) p 1145 3706 a(of) p 1252 3706 a(\(4.8\)) p Fp 1447 3706 a(\)) p Fh 824 3883 a(\024) p Fp 920 3883 a(2) p Fn(d) p Fi 1116 3802 a(X) p Fj 1028 4001 a(z) p Fc 1061 4010 a(1) p Fj 1095 4001 a(;z) p Fc 1148 4010 a(2) p Fm 1182 4001 a(2) p Fg(Z) p 1244 4001 a(Z) p Ff 1288 3975 a(d) p Fi 1324 3789 a(\020) p Fe 1373 3883 a(E) p Fh(j) p Fn(e) p Fj 1509 3845 a(isH) p Ff 1624 3853 a(!) p Fp 1673 3883 a(\() p Fn(!) p Fp 1783 3883 a(;) p Fn 1823 3883 a(x;) p 1915 3883 a(z) p Fl 1957 3897 a(1) p Fp 1998 3883 a(\)) p Fh(j) p Fl 2058 3845 a(3) p Fi 2098 3789 a(\021) p Fl 2148 3812 a(1) p Fj(=) p Fl(3) p Fh 2278 3883 a(\002) 1010 4176 y(\002) p Fi 1081 4082 a(\020) p Fe 1130 4176 a(E) p Fh(j) p Fn(@) p Fl 1272 4190 a(1) p Fn 1312 4176 a(H) p Fj 1388 4190 a(!) p Fp 1438 4176 a(\() p Fn(!) p Fp 1548 4176 a(;) p Fn 1588 4176 a(z) p Fl 1630 4190 a(1) p Fn 1670 4176 a(;) p 1710 4176 a(z) p Fl 1752 4190 a(2) p Fp 1792 4176 a(\)) p Fh(j) p Fl 1852 4138 a(3) p Fi 1892 4082 a(\021) p Fl 1942 4105 a(1) p Fj(=) p Fl(3) p Fi 2052 4082 a(\020) p Fe 2101 4176 a(E) p Fh(j) p Fn(e) p Fm 2237 4138 a(\000) p Fj(isH) p Ff 2407 4146 a(!) p Fp 2456 4176 a(\() p Fn(!) p Fp 2566 4176 a(;) p Fn 2606 4176 a(z) p Fl 2648 4190 a(2) p Fn 2689 4176 a(;) p 2729 4176 a(y) p Fp 2777 4176 a(\)) p Fh(j) p Fl 2837 4138 a(3) p Fi 2877 4082 a(\021) p Fl 2926 4105 a(1) p Fj(=) p Fl(3) p Fn 3036 4176 a(:) 448 4403 y @beginspecial @setspecial @endspecial Fo(By) p 589 4403 a(\(4.6\)) p 817 4403 a(and) p 993 4403 a(the) p 1144 4403 a(fact) p 1323 4403 a(that) p Fh 1509 4403 a(j) p Fn(e) p Fj 1576 4370 a(isH) p Ff 1691 4378 a(!) p Fp 1740 4403 a(\() p Fn(!) p Fp 1850 4403 a(;) p Fn 1890 4403 a(x;) p 1982 4403 a(y) p Fp 2030 4403 a(\)) p Fh(j) p 2117 4403 a(\024) p 2213 4403 a(k) p Fn(e) p Fj 2300 4370 a(isH) p Ff 2415 4378 a(!) p Fh 2464 4403 a(k) p Fj 2509 4417 a(op) p Fp 2609 4403 a(=) p 2705 4403 a(1) p Fo(,) p 2811 4403 a(we) p 2945 4403 a(have) p Fe 917 4616 a(E) p Fh(j) p Fn(e) p Fj 1053 4579 a(is) p Fm(L) p Ff 1159 4590 a(H) 1209 4598 y(!) p Fp 1261 4616 a(\() p Fn(@) p Fl 1344 4630 a(1) p Fn 1384 4616 a(H) p Fj 1460 4630 a(!) p Fp 1510 4616 a(\)\() p Fn(!) p Fp 1656 4616 a(;) p Fn 1696 4616 a(x;) p 1788 4616 a(y) p Fp 1836 4616 a(\)) p Fh(j) p Fl 1896 4579 a(2) p Fh 1962 4616 a(\024) p Fn 2058 4616 a(C) p 2130 4616 a(e) p Fm 2172 4579 a(\000) p Fj(\026) p Fm(j) p Fj(x) p Fm(\000) p Fj(y) p Fm 2421 4579 a(j) p Fn 2444 4616 a(;) p 2578 4616 a(x;) p 2670 4616 a(y) p Fh 2743 4616 a(2) p Fk 2829 4616 a(Z) p 2848 4616 a(Z) p Fj 2903 4579 a(d) p Fn 2943 4616 a(;) 448 4829 y @beginspecial @setspecial @endspecial Fo(for) p 587 4829 a(some) p 812 4829 a(c) p 849 4829 a(onstants) p Fn 1205 4829 a(C) p 1302 4829 a(>) p Fp 1398 4829 a(0) p Fo(,) p Fn 1499 4829 a(\026) p 1579 4829 a(>) p Fp 1675 4829 a(0) p Fo(.) p 1787 4829 a(Ther) p 1973 4829 a(efor) p 2122 4829 a(e,) p Fp 2221 4829 a([) p Fn(x) p Fl 2298 4843 a(1) p Fn 2338 4829 a(;) p 2378 4829 a(e) p Fj 2420 4796 a(is) p Fm(L) p Ff 2526 4807 a(H) 2576 4815 y(!) p Fp 2629 4829 a(\() p Fn(@) p Fl 2712 4843 a(1) p Fn 2752 4829 a(H) p Fj 2828 4843 a(!) p Fp 2878 4829 a(\)]) p Fo 2964 4829 a(is) p 3055 4829 a(uniformly) 448 4954 y(b) p 485 4954 a(ounde) p 714 4954 a(d) p 794 4954 a(in) p Fh 906 4954 a(L) p Fl 969 4921 a(2) p Fo 1041 4954 a(w.r.t.) p Fn 1295 4954 a(s) p Fh 1363 4954 a(2) p Fp 1449 4954 a(I) p 1467 4954 a(R) p Fo 1533 4954 a(,) p 1594 4954 a(and) p 1770 4954 a(we) p 1905 4954 a(c) p 1942 4954 a(onclude) p 2274 4954 a(\(4.7\).) p Fp 1897 5225 a(40) p eop %%Page: 41 41 41 40 bop Fq 448 573 a(References) p Fr 490 755 a([1]) p 623 755 a @beginspecial @setspecial @endspecial(Aizenman,) p 1054 755 a(M.,) p Fa 1222 755 a(L) l(o) l(c) l(alization) p 1693 755 a(at) p 1806 755 a(We) l(ak) p 2047 755 a(Disor) l(der:) p 2448 755 a(Some) p 2686 755 a(Elementary) p 3143 755 a(Bounds,) p Fr 623 854 a(Rev.) p 815 854 a(Math.) p 1062 854 a(Ph) n(ys.) p Fs 1290 854 a(6) p Fr(\(1994\),) p 1619 854 a(1163-1182.) 490 1003 y([2]) p 623 1003 a @beginspecial @setspecial @endspecial(Aizenman,) p 1032 1003 a(M.,) p 1178 1003 a(Graf,) p 1389 1003 a(G.) p 1501 1003 a(M.,) p Fa 1647 1003 a(L) l(o) l(c) l(alization) p 2100 1003 a(Bounds) p 2393 1003 a(for) p 2522 1003 a(an) p 2636 1003 a(Ele) l(ctr) l(on) p 2959 1003 a(Gas,) p Fr 3149 1003 a(J.) p 3237 1003 a(Ph) n(ys.) 623 1103 y(A:) p 736 1103 a(Math.) p 983 1103 a(Gen.) p Fs 1182 1103 a(31) p Fr(\(1998\),) p 1558 1103 a(6783-6806.) 490 1251 y([3]) p 623 1251 a @beginspecial @setspecial @endspecial(Aizenman,) p 1036 1251 a(M.,) p 1187 1251 a(Molc) n(hano) n(v,) p 1630 1251 a(S.,) p Fa 1751 1251 a(L) l(o) l(c) l(alization) p 2209 1251 a(at) p 2309 1251 a(L) l(ar) l(ge) p 2537 1251 a(Disor) l(der) p 2878 1251 a(and) p 3039 1251 a(at) p 3140 1251 a(Extr) l(eme) 623 1351 y(Ener) l(gies:) p 994 1351 a(A) n(n) p 1129 1351 a(Elementary) p 1572 1351 a(Derivation,) p Fr 2009 1351 a(Comm) n(un.) p 2388 1351 a(Math.) p 2634 1351 a(Ph) n(ys.) p Fs 2861 1351 a(157) p Fr(\(1993\),) p 3285 1351 a(245-) 623 1450 y(278.) 490 1599 y([4]) p 623 1599 a @beginspecial @setspecial @endspecial (Aizenman,) p 1055 1599 a(M.,) p 1224 1599 a(Sc) n(henk) n(er,) p 1615 1599 a(J.,) p 1751 1599 a(F) p 1798 1599 a(riedric) n(h,) p 2143 1599 a(R.,) p 2297 1599 a(and) p 2474 1599 a(Hundertmark,) p 3033 1599 a(D.,) p Fa 3190 1599 a(Finite-) 623 1699 y(volume) p 919 1699 a(fr) l(actional) p 1306 1699 a(moment) p 1640 1699 a(criteria) p 1952 1699 a(for) p 2099 1699 a(A) n(nderson) p 2487 1699 a(lo) l(c) l(alization,) p Fr 2961 1699 a(to) p 3078 1699 a(app) r(ear) p 3368 1699 a(in) 623 1798 y(Comm) n(un.) p 1003 1798 a(Math.) p 1250 1798 a(Ph) n(ys.) 490 1947 y([5]) p 623 1947 a @beginspecial @setspecial @endspecial(Anderson,) p 1017 1947 a(P) p 1067 1947 a(.) p 1117 1947 a(W.,) p Fa 1276 1947 a(A) n(bsenc) l(e) p 1594 1947 a(of) p 1691 1947 a(di\013usion) p 2032 1947 a(in) p 2133 1947 a(c) l(ertain) p 2411 1947 a(r) l(andom) p 2713 1947 a(lattic) l(es,) p Fr 3045 1947 a(Ph) n(ys.) p 3272 1947 a(Rev.) p Fs 623 2047 a(109) p Fr(\(1958\),) p 1047 2047 a(1492-1505.) 490 2195 y([6]) p 623 2195 a @beginspecial @setspecial @endspecial(Avron,) p 896 2195 a(J.) p 984 2195 a(E.,) p 1110 2195 a(Seiler,) p 1355 2195 a(R.,) p 1486 2195 a(and) p 1642 2195 a(Simon,) p 1915 2195 a(B.) p Fa 2019 2195 a(Char) l(ge) p 2295 2195 a(de\014ciency,) p 2701 2195 a(char) l(ge) p 2956 2195 a(tr) l(ansp) l(ort) p 3306 2195 a(and) 623 2295 y(c) l(omp) l(arison) p 1061 2295 a(of) p 1159 2295 a(dimensions,) p Fr 1645 2295 a(Comm) n(un.) p 2025 2295 a(Math.) p 2272 2295 a(Ph) n(ys.) p Fs 2499 2295 a(159) p Fr(\(1994\),) p 2924 2295 a(399-422.) 490 2443 y([7]) p 623 2443 a @beginspecial @setspecial @endspecial(Ben) n(tosela,) p 1023 2443 a(F.,) p 1153 2443 a(Carmona,) p 1538 2443 a(R.,) p 1675 2443 a(Duclos,) p 1971 2443 a(P) p 2021 2443 a(.,) p 2097 2443 a(Simon,) p 2375 2443 a(B.,) p 2510 2443 a(Souillard,) p 2886 2443 a(B.,) p 3020 2443 a(and) p 3183 2443 a(W) p 3261 2443 a(eder,) 623 2543 y(R.,) p Fa 764 2543 a(Schr\177) p 926 2543 a(odinger) p 1230 2543 a(op) l(er) l(ators) p 1595 2543 a(with) p 1781 2543 a(an) p 1904 2543 a(ele) l(ctric) p 2197 2543 a(\014eld) p 2380 2543 a(and) p 2546 2543 a(r) l(andom) p 2853 2543 a(or) p 2965 2543 a(deterministic) 623 2643 y(p) l(otentials,) p Fr 1020 2643 a(Comm) n(un.) p 1400 2643 a(Math.) p 1647 2643 a(Ph) n(ys.) p Fs 1875 2643 a(88) p Fr(\(1983\),) p 2251 2643 a(387-397.) 490 2791 y([8]) p 623 2791 a @beginspecial @setspecial @endspecial(Bellissard,) p 1024 2791 a(J.,) p 1139 2791 a(v) p 1178 2791 a(an) p 1293 2791 a(Elst,) p 1488 2791 a(A.,) p 1623 2791 a(Sc) n(h) n (ultz-Baldes,) p 2203 2791 a(H.,) p Fa 2339 2791 a(The) p 2508 2791 a(Non-Commutative) p 3199 2791 a(Ge) l(om-) 623 2891 y(etry) p 794 2891 a(of) p 891 2891 a(The) p 1061 2891 a(Quantum) p 1428 2891 a(Hal) t(l) p 1609 2891 a(E\013e) l(ct,) p Fr 1898 2891 a(J.) p 1992 2891 a(Math.) p 2239 2891 a(Ph) n(ys.) p Fs 2466 2891 a(35\(10\)) p Fr(\(1994\),) p 3013 2891 a(5373-5451.) 490 3039 y([9]) p 623 3039 a @beginspecial @setspecial @endspecial(F) p 670 3039 a(r\177) p 703 3039 a(ohlic) n(h,) p 974 3039 a(J.,) p 1097 3039 a(Sp) r(encer,) p 1438 3039 a(T.,) p Fa 1578 3039 a(A) n(bsenc) l(e) p 1901 3039 a(of) p 2004 3039 a(di\013usion) p 2350 3039 a(in) p 2456 3039 a(the) p 2599 3039 a(A) n(nderson) p 2978 3039 a(tight) p 3174 3039 a(binding) 623 3139 y(mo) l(del) p 860 3139 a(for) p 993 3139 a(lar) l(ge) p 1193 3139 a(disor) l(der) p 1513 3139 a(or) p 1620 3139 a(low) p 1769 3139 a(ener) l(gy,) p Fr 2054 3139 a(Comm) n(un.) p 2434 3139 a(Math.) p 2681 3139 a(Ph) n(ys.) p Fs 2908 3139 a(88) p Fr(\(1983\),) p 3285 3139 a(151-) 623 3239 y(184.) 448 3387 y([10]) p 623 3387 a @beginspecial @setspecial @endspecial(Kunz,) p 881 3387 a(H.,) p 1032 3387 a(Souillard,) p 1419 3387 a(B.,) p Fa 1566 3387 a(Sur) p 1732 3387 a(le) p 1832 3387 a(sp) l(e) l(ctr) l(e) p 2113 3387 a(les) p 2246 3387 a(op) n(\023) p 2330 3387 a(er) l(ateurs) p 2662 3387 a(aux) p 2827 3387 a(di\013) n(\023) p 2945 3387 a(er) l(enc) l(es) p 3246 3387 a(\014nies) 623 3487 y(al) n(\023) p 686 3487 a(eatoir) l(es,) p Fr 1048 3487 a(Comm) n(un.) p 1429 3487 a(Math.) p 1676 3487 a(Ph) n(ys.) p Fs 1903 3487 a(78) p Fr(\(1980\),) p 2280 3487 a(201-246.) 448 3636 y([11]) p 623 3636 a @beginspecial @setspecial @endspecial(Nak) p 766 3636 a(am) n(ura,) p 1050 3636 a(S.,) p Fa 1174 3636 a(L) l(e) l(ctur) l(es) p 1502 3636 a(on) p 1625 3636 a(Schr\177) p 1787 3636 a(odinger) p 2089 3636 a(Op) l(er) l(ators,) p Fr 2498 3636 a(Lectures) p 2836 3636 a(in) p 2937 3636 a(Mathematical) 623 3735 y(Sciences,) p 969 3735 a(Univ) n(ersit) n(y) p 1369 3735 a(of) p 1464 3735 a(T) p 1517 3735 a(oky) n(o,) p 1736 3735 a(1994.) 448 3884 y([12]) p 623 3884 a @beginspecial @setspecial @endspecial(Nak) p 766 3884 a(ano,) p 950 3884 a(F.,) p 1082 3884 a(and) p 1247 3884 a(Kaminaga,) p 1671 3884 a(M.,) p Fa 1825 3884 a(A) n(bsenc) l(e) p 2147 3884 a(of) p 2247 3884 a(tr) l(ansp) l(ort) p 2605 3884 a(under) p 2844 3884 a(a) p 2920 3884 a(slow) t(ly) p 3171 3884 a(varying) 623 3983 y(p) l(otential) p 962 3983 a(in) p 1064 3983 a(disor) l(der) l(e) l(d) p 1457 3983 a(systems,) p Fr 1786 3983 a(J.) p 1879 3983 a(Stat.) p 2082 3983 a(Ph) n(ys.) p Fs 2310 3983 a(97) p Fr(\(1999\),) p 2686 3983 a(917-940.) 448 4132 y([13]) p 623 4132 a @beginspecial @setspecial @endspecial(Sc) n(h) n(ultz-Baldes,) p 1197 4132 a(H.,) p 1326 4132 a(Bellissard,) p 1720 4132 a(J.,) p Fa 1830 4132 a(A) n(nomalous) p 2253 4132 a(tr) l(ansp) l(ort:) p 2637 4132 a(a) p 2701 4132 a(mathematic) l(al) p 3203 4132 a(fr) l(ame-) 623 4232 y(work) p Fr(,) p 844 4232 a(Rev.) p 1037 4232 a(Math.) p 1284 4232 a(Ph) n(ys.) p Fs 1511 4232 a(10) p Fr(\(1998\),) p 1888 4232 a(1-46.) 448 4380 y([14]) p 623 4380 a @beginspecial @setspecial @endspecial(Sc) n (h) n(ultz-Baldes,) p 1211 4380 a(H.,) p 1355 4380 a(Bellissard,) p 1764 4380 a(J.,) p Fa 1889 4380 a(A) p 1986 4380 a(Kinetic) p 2287 4380 a(The) l(ory) p 2576 4380 a(for) p 2714 4380 a(Quantum) p 3087 4380 a(T) p 3140 4380 a(r) l(ansp) l(ort) 623 4480 y(in) p 725 4480 a(Ap) l(erio) l(dic) p 1097 4480 a(Me) l(dia) p Fr(,) p 1367 4480 a(J.) p 1460 4480 a(Stat.) p 1663 4480 a(Ph) n(ys.) p Fs 1891 4480 a(91) p Fr(\(1998\),) p 2268 4480 a(991-1026.) 448 4628 y([15]) p 623 4628 a @beginspecial @setspecial @endspecial(Simon,) p 904 4628 a(B.,) p 1040 4628 a(and) p 1205 4628 a(Sp) r(encer,) p 1543 4628 a(T.,) p Fa 1681 4628 a(T) p 1734 4628 a(r) l(ac) l(e) p 1912 4628 a(class) p 2114 4628 a(p) l(erturb) l(ations) p 2617 4628 a(and) p 2781 4628 a(the) p 2922 4628 a(absenc) l(e) p 3226 4628 a(of) p 3327 4628 a(ab-) 623 4728 y(solutely) p 922 4728 a(c) l(ontinuous) p 1340 4728 a(sp) l(e) l(ctr) l(a,) p Fr 1668 4728 a(Comm) n(un.) p 2048 4728 a(Math.) p 2295 4728 a(Ph) n(ys.) p Fs 2523 4728 a(125) p Fr(\(1989\),) p 2947 4728 a(113-125.) 448 4877 y([16]) p 623 4877 a @beginspecial @setspecial @endspecial(v) n(on) p 783 4877 a(Dreifus,) p 1098 4877 a(H.,) p 1239 4877 a(Krein,) p 1497 4877 a(A.,) p Fa 1637 4877 a(A) p 1732 4877 a(new) p 1905 4877 a(pr) l(o) l(of) p 2117 4877 a(of) p 2218 4877 a(lo) l(c) l(alization) p 2652 4877 a(in) p 2757 4877 a(the) p 2898 4877 a(A) n(nderson) p 3276 4877 a(tight) 623 4976 y(binding) p 916 4976 a(mo) l(del,) p Fr 1206 4976 a(Comm) n(un.) p 1587 4976 a(Math.) p 1834 4976 a(Ph) n(ys.) p Fs 2061 4976 a(124) p Fr(\(1989\),) p 2486 4976 a(285-299.) p Fp 1897 5225 a(41) p eop %%Page: 42 42 42 41 bop 448 573 a @beginspecial @setspecial @endspecial Fr(Author's) p 793 573 a(address:) 448 743 y @beginspecial @setspecial @endspecial(F) p 495 743 a(umihik) n(o) p 814 743 a(Nak) p 957 743 a(ano) 448 843 y(Mathematical) p 976 843 a(Institute,) p 1339 843 a(T) p 1392 843 a(ohoku) p 1639 843 a(Univ) n(ersit) n(y) p 2005 843 a(,) 448 943 y(Sendai,) p 739 943 a(980-8578,) p 1108 943 a(JAP) p 1263 943 a(AN) 448 1042 y(e-mail:) p 730 1042 a(nak) p 857 1042 a(ano@math.tohoku.ac.jp) p Fp 1897 5225 a(42) p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0202140301457--