Content-Type: multipart/mixed; boundary="-------------0005260704833" This is a multi-part message in MIME format. ---------------0005260704833 Content-Type: text/plain; name="00-244.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="00-244.keywords" Resolvent Kernels, Thresholds, Stratified Media. ---------------0005260704833 Content-Type: application/postscript; name="gui.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="gui.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: gui.dvi %%Pages: 19 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips -o gui.ps gui.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2000.05.18:1748 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def 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6 6 5 bop 0 289 a Fn(Note)33 b(that)f(the)h(exp)s(onen)m(t)h(of)e Fk( )37 b Fn(v)-5 b(anishes)33 b(at)f Fk(k)f Fn(=)c Fl(\006)2030 262 y Fn(~)2027 289 y Fk(k)t Fn(,)32 b(where)0 509 y(\(2)p Fk(:)p Fn(4\))885 482 y(~)882 509 y Fk(k)f Fn(=)1070 482 y(~)1068 509 y Fk(k)s Fn(\()p Fk(p)p Fn(\))c(=)h(\()p Fk(c)1458 468 y Fj(2)1458 533 y Fh(\000)1517 509 y Fk(c)1559 468 y Fh(\000)p Fj(2)1559 533 y(+)1675 509 y Fl(\000)23 b Fn(1\))1862 468 y Fj(1)p Fg(=)p Fj(2)1972 509 y Fk(p;)2164 482 y Fn(~)2162 509 y Fk(k)31 b Fl(\025)d Fn(0)p Fk(;)0 729 y Fn(so)33 b(that)0 949 y(\(2)p Fk(:)p Fn(5\))391 b Fk( )t Fn(\()p Fk(y)t Fn(;)17 b Fk(k)s(;)g(p)p Fn(\))26 b(=)i(exp)q([)p Fl(\000)p Fk(ic)1436 964 y Fj(+)1495 949 y Fk(c)1537 908 y Fh(\000)p Fj(1)1537 973 y Fh(\000)1632 949 y Fn(\()p Fk(k)1724 908 y Fj(2)1785 949 y Fl(\000)1888 922 y Fn(~)1885 949 y Fk(k)1939 908 y Fj(2)1979 949 y Fn(\))2017 908 y Fj(1)p Fg(=)p Fj(2)2126 949 y Fk(y)t Fn(])p Fk(;)114 b(y)31 b(<)c Fl(\000)p Fk(y)2653 964 y Fg(c)2688 949 y Fk(:)0 1169 y Fn(Fix)j Fk(L)e(>)g Fn(0,)j Fk(a)d(>)f Fn(0.)43 b(F)-8 b(or)30 b(an)m(y)i Fk(p)c Fl(2)g Fn([0)p Fk(;)17 b(L)p Fn(])31 b(tak)m(e)h Fk(I)1803 1184 y Fg(p)1842 1169 y Fn(,)g(\012)1971 1133 y Fj(+)1971 1193 y Fg(p)2061 1169 y Fn(as)f(in)g(\(1.9\).)42 b(Note)31 b(that)g Fk(z)i Fl(2)28 b Fn(\012)3248 1133 y Fj(+)3248 1193 y Fg(p)0 1289 y Fn(implies)33 b Fk(k)j Fl(2)e Fi(C)587 1253 y Fj(+)676 1289 y Fl(\\)25 b(f)p Fn(Re)16 b Fi(k)34 b Fk(>)e Fi(0)p Fl(g)p Fn(.)53 b(Ho)m(w)m(ev)m(er,)39 b(using)c(the)h(asymptotic)f(b)s(eha)m(vior)h(\(2.3\))0 1409 y(for)31 b Fk(')p Fn(,)h Fk( )t Fn(,)g(it)e(is)i(ob)m(vious)f (that)h(b)s(oth)f(functions)h(can)g(b)s(e)g(extended)h(to)f Fk(k)e Fl(2)p 2820 1329 131 4 v 29 w Fi(C)2885 1381 y Fj(+)2951 1409 y Fn(,)h(so)h(that)0 1530 y(they)41 b(solv)m(e)g (\(2.2\))f(with)h Fk(z)46 b Fn(=)41 b Fk(c)1196 1494 y Fj(2)1196 1555 y(+)1255 1530 y Fn(\()p Fk(k)1347 1494 y Fj(2)1414 1530 y Fn(+)27 b Fk(p)1566 1494 y Fj(2)1606 1530 y Fn(\).)67 b(In)41 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b(d)47 b Fn(\()p Fk(y)t(;)17 b(p)p Fn(\))50 b Fl(2)0 2314 y Fi(R)33 b Fl(\002)23 b Fn([)p Fi(0)p Fk(;)17 b Fi(L)5 b Fn(])p Fc(.)0 2518 y Fn(\(Remark)33 b(that)g(for)f(the)i(con)m(tin)m(uit)m(y)f(of)g Fk( )k Fn(for)c(real)f Fk(k)g(<)d Fl(\000)2217 2492 y Fn(~)2214 2518 y Fk(k)36 b Fn(one)e(tak)m(es)g(in)f(\(2.3\),)g(\(2.5\))0 2638 y(the)g(ro)s(ot)f(satisfying)f(arg)q([\()p Fk(k)1067 2602 y Fj(2)1129 2638 y Fn(+)22 b Fk(p)1276 2602 y Fj(2)1315 2638 y Fn(\))17 b Fk(c)1412 2602 y Fj(2)1412 2663 y(+)1471 2638 y Fk(c)1513 2597 y Fh(\000)p Fj(2)1513 2660 y Fh(\000)1629 2638 y Fl(\000)23 b Fk(p)1778 2602 y Fj(2)1817 2638 y Fn(])1844 2602 y Fj(1)p Fg(=)p Fj(2)1987 2638 y Fn(=)32 b(arg)q([\()p Fk(k)2351 2602 y Fj(2)2413 2638 y Fl(\000)2515 2612 y Fn(~)2512 2638 y Fk(k)2566 2602 y Fj(2)2606 2638 y Fn(\))2644 2602 y Fj(1)p Fg(=)p Fj(2)2754 2638 y Fn(])c(=)f Fk(\031)t Fn(\).)0 2842 y(F)-8 b(or)32 b(an)m(y)h(t)m(w)m(o)g (functions)g Fk(\034)11 b Fn(\()p Fk(y)t Fn(\),)32 b Fk(\022)s Fn(\()p Fk(y)t 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b(and)g(such)h(that)g Fl(\006)2055 1047 y Fn(~)2052 1073 y Fk(k)s Fn(\()p Fk(p)p Fn(\))39 b Fk(=)-60 b Fl(2)28 b Fn(\000)33 b Fc(for)f Fk(p)c Fl(2)g Fn([0)p Fk(;)17 b(L)p Fn(])p Fc(.)44 b(Then,)0 1293 y Fn(\(2)p Fk(:)p Fn(9\))825 b(sup)910 1364 y Fa(\0001)p Fd(<\021)r Fa(\024)p Fd(\030)q(<)p Fa(1)933 1421 y Fd(k)q Fa(2)p Fb(\000)p Fd(;p)p Fa(2)p Fb([0)p Fd(;L)p Fb(])1314 1293 y Fl(j)p Fk(')p Fn(\()p Fk(\030)5 b Fn(;)17 b Fk(k)s(;)g(p)p Fn(\))g Fk( )t Fn(\()p Fk(\021)t Fn(;)g Fk(k)s(;)g(p)p Fn(\))p Fl(j)24 b Fk(<)k Fl(1)p Fk(:)0 1630 y Fo(Pro)s(of.)97 b Fn(\(a\))33 b(Observ)m(e)h(that)f(if)e(Im)17 b Fk(k)31 b(>)c Fn(0,)33 b(Re)17 b Fk(k)31 b Fl(6)p Fn(=)c(0,)33 b(then)g Fk(z)g Fn(=)28 b(\()p Fk(k)2583 1594 y Fj(2)2644 1630 y Fn(+)23 b Fk(p)2792 1594 y Fj(2)2831 1630 y Fn(\))17 b Fk(c)2928 1594 y Fj(2)2928 1655 y(+)3019 1630 y Fn(is)32 b(non-)0 1750 y(real.)54 b(Th)m(us,)39 b(if)c Fk(')f Fn(=)g Fk(\013)q( )t Fn(,)j Fk(\013)d Fl(2)h Fi(C)20 b Fn(,)43 b(then)37 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846 y Fn(Since)35 b Fl(j)p Fk(k)s Fl(j)c Fn(=)h Fl(j)p Fk(z)t(c)625 805 y Fh(\000)p Fj(2)625 868 y(+)743 846 y Fl(\000)24 b Fk(p)893 810 y Fj(2)933 846 y Fl(j)961 810 y Fj(1)p Fg(=)p Fj(2)1105 846 y Fn(and)35 b Fl(j)p Fk(k)1379 810 y Fj(2)1442 846 y Fl(\000)1546 820 y Fn(~)1543 846 y Fk(k)1597 810 y Fj(2)1637 846 y Fl(j)1665 810 y Fj(1)p Fg(=)p Fj(2)1806 846 y Fn(=)d Fk(c)1956 805 y Fh(\000)p Fj(1)1956 868 y(+)2050 846 y Fk(c)2092 861 y Fh(\000)2151 846 y Fl(j)p Fk(z)t(c)2270 805 y Fh(\000)p Fj(2)2270 868 y Fh(\000)2389 846 y Fl(\000)24 b Fk(p)2539 810 y Fj(2)2578 846 y Fl(j)2606 810 y Fj(1)p Fg(=)p Fj(2)2716 846 y Fn(,)36 b(the)f(estimate)0 966 y(\(1.10\))30 b(follo)m(ws)g(from)g(\(2.27\),)h(\(2.28\),)f(whic)m (h)i(also)e(imply)f(the)j(same)e(estimates)h(for)g(the)0 1087 y(extension)i(to)g Fk(I)594 1102 y Fg(p)633 1087 y Fn(.)p 3251 1265 57 4 v 3251 1315 4 50 v 3304 1315 V 3251 1318 57 4 v 0 1593 a Fo(Remark)52 b(2.8)98 b Fn(Observ)m(e)48 b(that)d(the)i(fact)e(that)h(w)m(e)h(are)f(dealing)e(with)i(a)f(family) f(of)0 1714 y(op)s(erators)38 b Fk(H)518 1729 y Fg(p)558 1714 y Fn(,)i Fk(p)d Fl(2)h Fn([0)p Fk(;)17 b(L)p Fn(],)40 b(complicates)d(the)i(pro)s(of.)60 b(Indeed,)41 b(in)d(our)g(estimates) g(w)m(e)0 1834 y(had)32 b(to)f(accoun)m(t)i(for)e(the)h(v)-5 b(arious)31 b(p)s(ositions)f(of)1837 1808 y(~)1834 1834 y Fk(k)h Fn(=)2022 1808 y(~)2020 1834 y Fk(k)s Fn(\()p Fk(p)p Fn(\))g(\(approac)m(hing)g(0)h(as)f Fk(p)d Fl(!)f Fn(0\))0 1954 y(and)e Fk(i\020)258 1969 y Fg(j)294 1954 y Fn(\()p Fk(p)p Fn(\),)i(the)e(zeros)h(of)e(the)h(W)-8 b(ronskian)25 b([)p Fk(';)17 b( )t Fn(])g(\()p Fk(k)s(;)g(p)p Fn(\).)40 b(The)26 b(latter)e(could)g(also)g(v)-5 b(anish)0 2075 y(as)33 b Fk(p)f Fn(approac)m(hes)i(a)e(threshold.)0 2278 y(As)i(noted)g(in)e(Remark)h(1.1,)h(the)f(k)m(ernel)i(\010)1612 2293 y Fg(p)1652 2278 y Fn(\()p Fk(\030)5 b(;)17 b(\021)t Fn(;)g Fk(k)s Fn(\))31 b(is)i(con)m(tin)m(uous)i(at)e Fk(k)f Fn(=)2900 2252 y(~)2898 2278 y Fk(k)k Fn(if)c Fk(p)d(>)g Fn(0)0 2398 y(\(Claim)h(2.2)i(\(a\)\),)h(but)136 b(sup)883 2484 y Fj(\()p Fg(\030)s(;\021)r Fj(\))p Fh(2)p Fg(R)p Fh(\002)p Fg(R)1255 2398 y Fl(j)p Fn(\010)1353 2413 y Fg(p)1393 2398 y Fn(\()p Fk(\030)5 b(;)17 b(\021)t Fn(;)g Fk(k)s Fn(\))p Fl(j)30 b Fn(ma)m(y)j(blo)m(w-up)f(as)h Fk(k)i Fn(approac)m(hes)3063 2372 y(~)3060 2398 y Fk(k)s Fn(\()p Fk(p)p Fn(\).)0 2771 y Fo(Remark)54 b(2.9)97 b Fn(The)48 b(metho)s(d)f(used)h(here)g(can)g(clearly)e(b)s(e)h(used)h (in)f(the)g(study)i(of)0 2891 y(resolv)m(en)m(t)38 b(k)m(ernels)f(for)f (an)h(op)s(erator)f(of)g(the)h(form)e Fl(\000)2060 2852 y Fg(d)2096 2829 y Fb(2)p 2041 2868 109 4 v 2041 2926 a Fg(dy)2114 2907 y Fb(2)2184 2891 y Fn(+)25 b Fk(V)d Fn(\()p Fk(y)t Fn(\),)36 b(where)i Fk(V)21 b Fn(\()p Fk(y)t Fn(\))34 b(=)g Fk(V)3248 2906 y Fh(\006)0 3012 y Fn(for)e Fl(\006)p Fk(y)f(>)d(y)457 3027 y Fg(c)491 3012 y Fn(.)0 3215 y(The)35 b(case)f Fk(V)466 3230 y Fj(+)555 3215 y Fn(=)c Fk(V)718 3230 y Fh(\000)810 3215 y Fn(corresp)s(onds)35 b(to)f Fk(p)c Fn(=)f(0)34 b(while)f Fk(V)2047 3230 y Fh(\000)2135 3215 y Fk(>)d(V)2298 3230 y Fj(+)2390 3215 y Fn(corresp)s(onds)35 b(to)f Fk(p)c(>)f Fn(0.)0 3336 y(Similar)g(estimates)j(are)h(obtained)f(for)g(the)h(k)m (ernel)g(in)f(the)h(neigh)m(b)s(orho)s(o)s(d)e(of)h Fk(V)2995 3351 y Fh(\006)3054 3336 y Fn(.)0 3639 y Fo(Pro)s(of)54 b(of)g(Theorem)g(B.)46 b Fn(By)i(Claim)c(2.4)j(w)m(e)h(ha)m(v)m(e,)k (for)47 b(0)52 b Fk(<)g(\016)k(<)2818 3599 y Fj(1)p 2818 3616 36 4 v 2818 3673 a(2)2882 3612 y Fn(~)2880 3639 y Fk(k)s Fn(\()p Fk(`)p Fn(\),)50 b(that)0 3759 y Fk(')p Fn(\()p Fk(y)t Fn(;)17 b Fk(k)s(;)g(p)p Fn(\),)27 b Fk( )t Fn(\()p Fk(y)t Fn(;)17 b Fk(k)s(;)g(p)p Fn(\))27 b(and)h(their)f Fk(y)t Fn(-deriv)-5 b(ativ)m(es)27 b(are)h(analytic)f(\(in)g Fk(k)s Fn(\))h(in)f(the)h(disk)h Fk(B)3166 3774 y Fg(\016)3231 3759 y Fn(=)0 3879 y Fl(fj)p Fk(k)s Fl(j)k Fk(<)g(\016)t Fl(g)p Fn(.)54 b(In)36 b(particular,)f(the)i(deriv)-5 b(ativ)m(e)1738 3840 y Fg(@)p 1718 3856 80 4 v 1718 3914 a(@)t(k)1825 3879 y Fn([)p Fk(';)17 b( )t Fn(])g(\()p Fk(k)s(;)g(p)p Fn(\))35 b(is)g(b)s(ounded)i(for)e(\()p Fk(k)s(;)17 b(p)p Fn(\))34 b Fl(2)0 4000 y Fk(B)74 4015 y Fg(\016)134 4000 y Fl(\002)23 b Fn([)p Fk(`;)17 b(L)p Fn(].)43 b(This)33 b(implies,)d(in)i(view)h(of)f(\(2.12\),)g(that)g (for)g(some)h(0)27 b Fk(<)h(")f(<)2821 3960 y Fg(\031)p 2821 3977 43 4 v 2825 4034 a Fj(2)2874 4000 y Fn(,)0 4220 y(\(2)p Fk(:)p Fn(29\))152 b Fl(j)p Fn([)p Fk(';)17 b( )t Fn(])g(\()p Fk(k)s(;)g(p)p Fn(\))p Fl(j)26 b(\025)i Fk(\015)5 b Fl(j)p Fk(k)s Fl(j)p Fk(;)114 b(k)31 b Fl(2)d Fk(B)1620 4179 y Fg(")1615 4244 y(\016)1684 4220 y Fn(:=)g Fk(B)1889 4235 y Fg(\016)1949 4220 y Fl(\\)23 b(fj)17 b Fn(arg)33 b Fk(k)s Fl(j)27 b Fk(<)h(")p Fl(g)p Fk(;)113 b(p)28 b Fl(2)g Fn([)p Fk(`;)17 b(L)p Fn(])p Fk(;)0 4440 y Fn(where)36 b Fk(\015)f Fn(=)c Fk(\015)5 b Fn(\()p Fk(";)17 b(\016)n(;)g(`;)g(L)p Fn(\))30 b Fk(>)g Fn(0.)49 b(It)34 b(follo)m(ws)f(\(\(2.8\)\))h(that)g(\010)2219 4455 y Fg(p)2259 4440 y 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Fj(2)1525 4847 y Fn(\))p Fk(:)38 b Fn(Replacing)f(the)h Fk(k)s Fn(-deriv)-5 b(ativ)m(e)37 b(in)h(\(2.39\))f(b)m(y)0 4968 y Fk(\025)p Fn(-deriv)-5 b(ativ)m(e)27 b(w)m(e)j(obtain)d(\(1.13\).)42 b(Observ)m(e)30 b(that)e(outside)h(neigh)m(b)s(orho)s(o)s(ds)f(of)g Fk(c)2996 4931 y Fj(2)2996 4992 y Fh(\006)3055 4968 y Fk(p)3104 4931 y Fj(2)3172 4968 y Fn(the)0 5088 y(theorem)k(is)g(ob)m (vious.)p 3251 5267 57 4 v 3251 5316 4 50 v 3304 5316 V 3251 5319 57 4 v eop %%Page: 15 15 15 14 bop 0 289 a Fe(App)t(endix)0 591 y Fn(In)38 b(this)g(app)s(endix) g(w)m(e)g(sho)m(w)h(ho)m(w)g(the)f(decomp)s(osition)e(\(1.3\)-\(1.7\),) i(com)m(bined)f(with)0 711 y(estimates)30 b(on)g(the)h(k)m(ernel)g Fk(L)1077 726 y Fg(p)1117 711 y Fn(,)g(leads)f(to)g(estimates)f(on)i (the)f(b)s(eha)m(vior)g(of)g(the)h(resolv)m(en)m(t)0 832 y(of)h(the)i(Laplacian)d Fl(\000)p Fn(\001)i(near)g(the)h(lo)m(w)m (er)e(endp)s(oin)m(t)h(of)g(its)f(sp)s(ectrum,)h Fk(\025)28 b Fn(=)g(0.)44 b(F)-8 b(or)32 b(this)0 952 y(purp)s(ose,)h(w)m(e)h (shall)d(use)j(only)e(the)h(global)d(b)s(ound)j(of)f Fk(L)2081 967 y Fg(p)2121 952 y Fn(.)0 1155 y(F)-8 b(or)32 b Fk(\033)f Fl(2)e Fi(R)43 b Fn(w)m(e)34 b(denote)f(b)m(y)g Fk(L)1119 1119 y Fj(2)p Fg(;\033)1222 1155 y Fn(\()p Fi(R)1325 1119 y Ff(n)1390 1155 y Fn(\))g(the)g(w)m(eigh)m(ted)p Fl(\000)p Fk(L)2145 1119 y Fj(2)2219 1155 y Fn(space)g(normed)g(b)m(y) 848 1422 y Fl(jj)p Fk(f)11 b Fl(jj)1019 1381 y Fj(2)1019 1448 y Fg(L)1067 1429 y Fb(2)p Fd(;\033)1157 1448 y Fj(\()p Fg(R)1237 1429 y Fd(n)1280 1448 y Fj(\))1340 1422 y Fn(=)1443 1287 y Fm(Z)1499 1512 y Fg(R)1552 1493 y Fd(n)1599 1422 y Fn(\(1)22 b(+)g Fl(j)p Fk(x)p Fl(j)1917 1381 y Fj(2)1956 1422 y Fn(\))1994 1381 y Fg(\033)2041 1422 y Fl(j)p Fk(f)11 b Fn(\()p Fk(x)p Fn(\))p Fl(j)2287 1381 y Fj(2)2325 1422 y Fk(dx:)0 1704 y Fn(Since)33 b Fl(j)p Fk(L)349 1719 y Fg(p)388 1704 y Fn(\()p Fk(\030)5 b(;)17 b(\021)t Fn(;)g Fk(z)t Fn(\))p Fl(j)27 b(\024)h Fk(C)7 b Fl(j)p Fk(z)27 b Fl(\000)22 b Fk(p)1186 1668 y Fj(2)1226 1704 y Fl(j)1254 1668 y Fh(\000)p Fj(1)p Fg(=)p Fj(2)1418 1704 y Fn(,)33 b(w)m(e)g(get)0 1970 y(\(A)p Fk(:)p Fn(1\))295 b Fl(jj)p Fk(M)670 1985 y Fg(p)710 1970 y Fn(\()p Fk(z)t Fn(\))p Fk(f)11 b Fl(jj)950 1987 y Fg(L)998 1968 y Fb(2)p Fd(;)p Fa(\000)p Fd(s)1128 1987 y Fj(\()p Fg(R)p Fj(\))1268 1970 y Fl(\024)28 b Fk(C)1443 1985 y Fg(s)1480 1970 y Fl(j)p Fk(z)e Fl(\000)d Fk(p)1728 1929 y Fj(2)1767 1970 y Fl(j)1795 1929 y Fh(\000)p Fj(1)p Fg(=)p Fj(2)1960 1970 y Fl(jj)p Fk(f)11 b Fl(jj)2131 1987 y Fg(L)2179 1968 y Fb(2)p Fd(;s)2260 1987 y Fj(\()p Fg(R)p Fj(\))2373 1970 y Fk(;)114 b(s)28 b(>)2701 1903 y Fn(1)p 2701 1947 49 4 v 2701 2039 a(2)2760 1970 y Fk(:)0 2220 y Fn(W)-8 b(e)34 b(shall)f(no)m(w)i(use)g(this)f(estimate)f(to)h(establish)f(an)h (estimate)g(for)f Fk(M)10 b Fn(\()p Fk(z)t Fn(\))36 b(near)e Fk(z)h Fn(=)30 b(0.)0 2340 y(So,)c(using)d(the)h(notation)f(in)g(the)h (In)m(tro)s(duction,)i(let)d Fk(f)11 b Fn(\()p Fk(x;)17 b(y)t Fn(\),)25 b Fk(g)t Fn(\()p Fk(x;)17 b(y)t 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b(Univ)m(ersit)m(\023)-46 b(e)43 b(de)244 5291 y(Pro)m(v)m(ence,)35 b(Marseille)c(1997.)p eop %%Page: 18 18 18 17 bop 49 289 a Fo(7.)49 b(A.)39 b(Boutet)g(de)h(Mon)m(v)m(el)f(and) i(D.)f(Manda)p Fn(,)c Fc(Sp)-5 b(e)g(ctr)g(al)36 b(and)g(sc)-5 b(attering)37 b(the)-5 b(ory)244 409 y(of)44 b(wave)g(pr)-5 b(op)g(agation)44 b(in)h(a)f(p)-5 b(erturb)g(e)g(d)45 b(str)-5 b(ati\014e)g(d)45 b(me)-5 b(dium)p Fn(,)45 b(J.)f(Math.)76 b(Anal.)244 529 y(Appl.)43 b(191)p 523 545 147 4 v 32 w(\(1995\),)31 b(137-167.)49 733 y Fo(8.)92 b(A.)56 b(Cohen)h(and)g(T.) f(Kapp)s(eler)p Fn(,)d Fc(Sc)-5 b(attering)50 b(and)f(inverse)g(sc)-5 b(attering)49 b(for)244 853 y(steplike)g(p)-5 b(otentials)48 b(in)h(the)h(Schr\177)-50 b(odinger)48 b(e)-5 b(quation)p Fn(,)52 b(Indiana)47 b(Univ.)91 b(Math.)244 974 y(J.)33 b(34)p 354 990 98 4 v 32 w(\(1985\),)e(127-180.)49 1177 y Fo(9.)42 b(E.)35 b(Cro)s(c)f(and)h(Y.)g(Dermenjian)p Fn(,)30 b Fc(A)n(nalyse)i(sp)-5 b(e)g(ctr)g(ale)32 b(d'une)h(b)-5 b(ande)31 b(ac)-5 b(oustique)244 1297 y(multistr)g(ati\014)n(\023)-47 b(ee,)38 b(Partie)h(I)f(:)h(Princip)-5 b(e)37 b(d'absorption)h(limite)g (p)-5 b(our)38 b(une)h(str)-5 b(ati\014-)244 1418 y(c)g(ation)34 b(simple)p Fn(,)e(SIAM)h(J.)g(Math.)44 b(Anal.)e(26)p 1832 1434 V 32 w(\(1995\),)32 b(880-924.)49 1621 y Fo(10.)67 b(S.)47 b(de)g(Bi)n(\022)-54 b(evre)46 b(and)h(D.W.)g(Pra)m(vica)p Fn(,)42 b Fc(Sp)-5 b(e)g(ctr)g(al)42 b(analysis)f(of)h(optic)-5 b(al)42 b(\014br)-5 b(es)244 1742 y(and)34 b(str)-5 b(ati\014e)g(d)35 b(\015uids)p Fn(,)244 1862 y(I.)98 b(J.)32 b(F)-8 b(unc.)44 b(Anal.)f(98)p 1065 1878 V 32 w(\(1991\),)31 b(404-436.)244 1982 y(I)s(I.)i(Comm.)42 b(PDE)33 b(17)p 969 1998 V 32 w(\(1992\),)e(69-97.)49 2186 y Fo(11.)64 b(Y.)44 b(Dermenjian)h(and)h (J.-C.)g(Guillot)p Fn(,)38 b Fc(Sc)-5 b(attering)41 b(of)g(elastic)f (waves)h(in)f(a)244 2306 y(p)-5 b(erturb)g(e)g(d)34 b(isotr)-5 b(opic)33 b(half)g(sp)-5 b(ac)g(e)33 b(with)h(a)f(fr)-5 b(e)g(e)34 b(b)-5 b(oundary.)44 b(The)33 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b(Eqs.)k(93)p 2886 3414 98 4 v 25 w(\(1991\),)244 3518 y(260-282.)49 3722 y Fo(15.)56 b(J.)42 b(Nemiro)m(vsky)p Fn(,)36 b Fc(Ele)-5 b(ctr)g(omagnetic)38 b(waves)g(in)g(layer)-5 b(e)g(d)39 b(anisotr)-5 b(opic)37 b(me)-5 b(dia)38 b(-)244 3842 y(a)d(sp)-5 b(e)g(ctr)g(al)34 b(the)-5 b(ory)p Fn(,)33 b(Ph.)44 b(D.)32 b(Thesis,)i(Hebrew)g(Univ)m (ersit)m(y)-8 b(,)33 b(Jerusalem)f(1998.)49 4045 y Fo(16.)43 b(S.)37 b(Shimizu)p Fn(,)30 b Fc(The)j(limiting)g(absorption)g (principle)g(for)h(elastic)f(wave)g(pr)-5 b(op)g(aga-)244 4166 y(tion)41 b(pr)-5 b(oblems)41 b(in)g(p)-5 b(erturb)g(e)g(d)42 b(str)-5 b(ati\014e)g(d)41 b(me)-5 b(dia)41 b Fi(R)2181 4130 y Ff(3)2242 4166 y Fn(,)g(Math.)66 b(Meth.)g(in)39 b(Appl.)244 4286 y(Sci.)k(19)p 439 4302 V 32 w(\(1996\),)32 b(187-215.)49 4490 y Fo(17.)240 4466 y(\023)232 4490 y(E.)45 b(So)s(ccorsi)p Fn(,)846 4464 y Fc(\023)831 4490 y(Etude)26 b(math)n(\023)-47 b(ematique)23 b(de)h(la)h(pr)-5 b(op)g(agation)24 b(des)g(ondes)e(\023)-47 b(ele)-5 b(ctr)g(omagn)n 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y(V)-8 b(erlag)31 b(1991.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0005260704833--