Content-Type: multipart/mixed; boundary="-------------0106211149626" This is a multi-part message in MIME format. ---------------0106211149626 Content-Type: text/plain; name="01-222.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="01-222.keywords" Random Magnetic Schr{\"o}dinger Operators, Density of States, Wegner estimate, Diamagnetic inequality. ---------------0106211149626 Content-Type: application/postscript; name="Wegner.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Wegner.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: Wegner.dvi %%Pages: 26 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Italic Times-Bold Times-Roman RMTMI MTSY MTEX %%+ Helvetica %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -D600 -y1200 Wegner.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2001.06.21:1829 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MTSY %!PS-AdobeFont-1.1: MTSY 1.1 %%CreationDate: 1993 May 30 16:26:28 % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation) readonly def /FullName (MTSY) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /MTSY def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 8 /circleplus put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 27 /propersuperset put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 54 /negationslash put dup 55 /mapsto put dup 59 /emptyset put dup 67 /plus put dup 68 /equal put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 110 /backslash put dup 112 /radical put dup 114 /nabla put dup 116 /unionsq put dup 117 /intersectionsq put readonly def /FontBBox{0 -954 1043 796}readonly def /UniqueXX 5018947 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d70c1e2528f01045f8caec9829f31d6 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FC(,)g(mp_arc)f(01-139)g (\(2001\),)e(by)i(P)-9 b(.)20 b(D.)0 2258 y(Hislop)g(and)g(F)-6 b(.)19 b(Klopp)h(e)o(xtends)g(part)g(of)f(this)h(result)h(to)f (single-site)g(potentials)h(taking)g(v)n(alues)f(of)g(both)f(signs.)0 2592 y FF(Refer)n(ences)102 2779 y FC(1.)50 b(Adler)m(,)19 b(R.J.:)h FB(The)g(g)o(eometry)h(of)f(r)o(andom)f(\002elds)p FC(.)h(Chichester:)h(W)m(ile)o(y)-5 b(,)21 b(1981)102 2872 y(2.)50 b(Ando,)20 b(T)-6 b(.,)22 b(F)o(o)n(wler)m(,)f(A.B.,)g (Stern,)h(F)-6 b(.:)22 b(Electronic)g(properties)g(of)f(tw)o (o-dimensional)h(systems.)g(Re)n(v)-5 b(.)22 b(Mod.)f(Phys.)212 2962 y Fe(54)p FC(,)e(437\226672)g(\(1982\))102 3054 y(3.)50 b(A)-6 b(vron,)24 b(J.,)h(Herbst,)g(I.,)g(Simon,)h(B.:)g (Schr\366dinger)f(operators)g(with)h(magnetic)g(\002elds.)h(I.)e (General)h(interactions.)212 3144 y(Duk)o(e)19 b(Math.)i(J.)e Fe(45)p FC(,)h(847\226883)f(\(1978\))102 3236 y(4.)50 b(Barbaroux,)22 b(J.-M.,)g(Combes,)h(J.M.,)f(Hislop,)h(P)-9 b(.D.:)22 b(Localization)j(near)e(band)f(edges)i(for)d(random)i (Schr\366dinger)212 3326 y(operators.)c(Helv)-5 b(.)20 b(Phys.)f(Acta)i Fe(70)p FC(,)e(16\22643)h(\(1997\))102 3419 y(5.)50 b(Barbaroux,)23 b(J.-M.,)f(Combes,)i(J.M.,)g(Hislop,)f(P) -9 b(.D.:)23 b(Landau)h(Hamiltonians)g(with)g(unbounded)f(random)g (poten-)212 3508 y(tials.)d(Lett.)h(Math.)f(Phys.)f Fe(40)p FC(,)h(335\226369)f(\(1997\))102 3601 y(6.)50 b(Bauer)m(,)26 b(H.:)h FB(Ma\337-)f(und)h(Inte)m(gr)o(ationstheorie)p FC(.)g(2.)f(Au\003age,)h(Berlin:)h(de)f(Gruyter)m(,)e(1992)h([in)h (German])f(English)212 3691 y(translation)20 b(to)g(appear)102 3783 y(7.)50 b(Bonch-Brue)n(vich,)22 b(V)-10 b(.L.,)21 b(Enderlein,)h(R.,)g(Esser)m(,)f(B.,)i(K)n(eiper)m(,)f(R.,)g(Mirono)o (v)-5 b(,)21 b(A.G.,)g(Zvyagin,)g(I.P)-9 b(.:)23 b FB(Elektr)l(onen-) 212 3873 y(theorie)18 b(ung)o(eor)m(dneter)g(Halbleiter)p FC(.)g(Berlin:)g(VEB)f(Deutscher)h(V)-9 b(erlag)17 b(der)g(W)m (issenschaften,)i(1984)e([in)g(German.)212 3963 y(Russian)j(original:)g (Mosco)n(w:)g(Nauka,)g(1981])102 4055 y(8.)50 b(Broderix,)25 b(K.,)h(Hundertmark,)g(D.,)g(Leschk)o(e,)h(H.:)f(Self-a)n(v)o(eraging,) h(decomposition)g(and)g(asymptotic)g(proper)n(-)212 4145 y(ties)f(of)f(the)g(density)h(of)f(states)h(for)f(random)g (Schr\366dinger)g(operators)g(with)g(constant)h(magnetic)h(\002eld.)f (In:)f FB(P)-6 b(ath)212 4235 y(inte)m(gr)o(als)24 b(fr)l(om)h(meV)f (to)g(MeV)-5 b(:)25 b(T)l(utzing)f('92)p FC(.)g(Grabert,)g(H.,)g (Inomata,)h(A.,)f(Schulman,)h(L.S.,)f(W)-6 b(eiss,)25 b(U.)f(\(eds.\),)212 4324 y(Singapore:)c(W)-6 b(orld)19 b(Scienti\002c,)j(1993,)d(pp.)h(98\226107)102 4417 y(9.)50 b(Broderix,)26 b(K.,)g(Hundertmark,)f(D.,)i(Leschk)o(e,)g(H.:)f (Continuity)h(properties)g(of)f(Schr\366dinger)g(semigroups)h(with)212 4507 y(magnetic)21 b(\002elds.)f(Re)n(v)-5 b(.)21 b(Math.)f(Phys.)f Fe(12)p FC(,)h(181\226225)f(\(2000\))62 4599 y(10.)50 b(Carmona,)19 b(R.,)g(Lacroix,)g(J.:)g FB(Spectr)o(al)h(theory)g(of)f (r)o(andom)f(Sc)o(hr\366ding)o(er)h(oper)o(ator)o(s)p FC(.)g(Boston:)g(Birkh\344user)m(,)g(1990)62 4692 y(11.)50 b(Combes,)18 b(J.M.,)f(Hislop,)g(P)-9 b(.D.:)18 b(Localization)i(for)c (some)j(continuous,)e(random)h(Hamiltonians)g(in)g FB(d)6 b FC(-dimensions.)212 4781 y(J.)19 b(Funct.)i(Anal.)f Fe(124)p FC(,)f(149\226180)g(\(1994\))62 4874 y(12.)50 b(Combes,)16 b(J.M.,)f(Hislop,)g(P)-9 b(.D.:)16 b(Landau)g (Hamiltonians)g(with)g(random)f(potentials:)i(Localization)g(and)f(the) g(density)212 4964 y(of)j(states.)i(Commun.)f(Math.)g(Phys.)f Fe(177)p FC(,)h(603\226629)f(\(1996\))62 5056 y(13.)50 b(Combes,)24 b(J.M.,)g(Hislop,)f(P)-9 b(.D.,)24 b(Mourre,)g(E.:)f (Spectral)j(a)n(v)o(eraging,)e(perturbation)g(of)g(singular)g(spectra,) h(and)f(lo-)212 5146 y(calization.)d(T)m(rans.)f(Am.)g(Math.)g(Soc.)g Fe(348)p FC(,)g(4883\2264894)e(\(1996\))62 5238 y(14.)50 b(Combes,)16 b(J.M.,)g(Schrader)m(,)g(R.,)g(Seiler)m(,)h(R.:)f (Classical)i(bounds)d(and)h(limits)h(for)e(ener)o(gy)h(distrib)n (utions)g(of)f(Hamilton)212 5328 y(operators)k(in)h(electromagnetic)i (\002elds.)f(Ann.)e(Phys.)h(\(N.Y)-10 b(.\))17 b Fe(111)p FC(,)j(1\22618)f(\(1978\))62 5421 y(15.)50 b(Craig,)25 b(W)-7 b(.,)25 b(Simon,)g(B.:)h(Log)f(H\366lder)f(continuity)i(of)f (the)g(inte)o(grated)h(density)g(of)e(states)j(for)d(stochastic)j (Jacobi)212 5510 y(matrices.)21 b(Commun.)e(Math.)h(Phys.)g Fe(90)p FC(,)g(207\226218)f(\(1983\))62 5603 y(16.)50 b(Cycon,)20 b(H.L.,)f(Froese,)h(R.G.,)g(Kirsch,)f(W)-7 b(.,)20 b(Simon,)g(B.:)g FB(Sc)o(hr\366ding)o(er)g(oper)o(ator)o(s)p FC(.)g(Berlin:)h(Springer)m(,)e(1987)62 5695 y(17.)50 b(Da)n(vies,)17 b(E.B.:)f FB(Heat)g(k)o(ernels)i(and)e(spectr)o(al)h (theory)p FC(.)g(P)o(aperback)g(edition,)g(Cambridge:)g(Cambridge)g (Uni)n(v)-5 b(.)15 b(Press,)212 5785 y(1990)p eop %%Page: 25 25 25 24 bop 458 20 a FC(Density)20 b(of)g(States)h(for)e(Random)h (Schr\366dinger)g(Operators)f(with)h(Magnetic)h(Fields)532 b(25)62 298 y(18.)50 b(Delyon,)20 b(F)-6 b(.,)20 b(Souillard,)h(B.:)f (Remark)h(on)f(the)h(continuity)g(of)f(the)h(density)g(of)e(states)j (of)e(er)o(godic)g(\002nite)h(dif)n(ference)212 388 y(operators.)e (Commun.)h(Math.)g(Phys.)g Fe(94)p FC(,)f(289\226291)g(\(1984\))62 475 y(19.)50 b(Doi,)20 b(S.,)h(Iw)o(atsuka,)f(A.,)h(Mine,)g(T)-6 b(.:)20 b(The)h(uniqueness)g(of)f(the)h(inte)o(grated)h(density)f(of)f (states)i(for)e(the)h(Schr\366dinger)212 565 y(operators)e(with)h (magnetic)h(\002elds.)g(Math.)f(Z.)g Fe(237)p FC(,)f(335\226371)g (\(2001\))62 652 y(20.)50 b(Dorlas,)20 b(T)-6 b(.C.,)20 b(Macris,)i(N.,)e(Pul\351,)h(J.V)-10 b(.:)21 b(Characterization)h(of)e (the)i(spectrum)f(of)f(the)h(Landau)g(Hamiltonian)h(with)212 742 y(delta)e(impurities.)h(Commun.)e(Math.)i(Phys.)e Fe(204)p FC(,)h(367\226396)f(\(1999\))62 829 y(21.)50 b(Droese,)39 b(J.,)h(Kirsch,)f(W)-7 b(.:)40 b(The)g(ef)n(fect)g(of)f (boundary)g(conditions)h(on)g(the)g(density)g(of)f(states)i(for)e (random)212 919 y(Schr\366dinger)19 b(operators.)h(Stochastic)h (Processes)g(Appl.)f Fe(23)p FC(,)f(169\226175)g(\(1986\))62 1006 y(22.)50 b(Fernique,)26 b(X.M.:)g(Re)o(gularit\351)h(des)g (trajectoires)h(des)e(fonctions)g(al\351atoires)i(Gaussiennes.)f(In:)f FB(Ecole)h(d'Et\351)f(de)212 1095 y(Pr)l(obabilit\351s)31 b(de)f(Saint-Flour)g(IV)g(-)g(1974)p FC(.)g(Hennequin,)g(P)-9 b(.-L.)30 b(\(ed.\),)g(Lecture)h(Notes)f(in)h(Mathematics)h Fe(480)p FC(,)212 1185 y(Berlin:)20 b(Springer)m(,)f(1975,)h(pp.)f (1\22696)h([in)f(French])62 1272 y(23.)50 b(Fischer)m(,)16 b(W)-7 b(.,)16 b(Hupfer)m(,)f(T)-6 b(.,)16 b(Leschk)o(e,)h(H.,)f (M\374ller)m(,)g(P)-9 b(.:)16 b(Existence)i(of)d(the)i(density)g(of)e (states)j(for)d(multi-dimensional)212 1362 y(continuum)21 b(Schr\366dinger)g(operators)g(with)g(Gaussian)g(random)g(potentials.)h (Commun.)f(Math.)g(Phys.)g Fe(190)p FC(,)g(133\226)212 1452 y(141)e(\(1997\))62 1539 y(24.)50 b(Fischer)m(,)29 b(W)-7 b(.,)29 b(Leschk)o(e,)h(H.,)e(M\374ller)m(,)h(P)-9 b(.:)30 b(Spectral)g(localization)h(by)e(Gaussian)h(random)e (potentials)i(in)g(multi-)212 1629 y(dimensional)20 b(continuous)g (space.)h(J.)f(Stat.)h(Phys.)e Fe(101)p FC(,)h(935\226985)f(\(2000\))62 1716 y(25.)50 b(F)o(ock,)17 b(V)-10 b(.:)16 b(Bemerkung)h(zur)f (Quantelung)h(des)g(harmonischen)g(Oszillators)g(im)g(Magnetfeld.)h(Z.) e(Physik)h Fe(47)p FC(,)f(446\226)212 1806 y(448)j(\(1928\))g([in)g (German])62 1893 y(26.)50 b(Gilbar)o(g,)17 b(D.,)g(T)m(rudinger)m(,)g (N.S.:)h FB(Elliptic)g(partial)g(dif)o(fer)m(ential)h(equations)f(of)g (second)h(or)m(der)p FC(.)f(2)2895 1864 y FD(nd)2978 1893 y FC(edition,)g(Berlin:)212 1983 y(Springer)m(,)h(1983)62 2070 y(27.)50 b(Gradshte)o(yn,)16 b(I.S.,)g(Ryzhik,)i(I.M.:)e FB(T)-7 b(able)17 b(of)g(inte)m(gr)o(als,)g(series,)h(and)e(pr)l (oducts)p FC(.)i(Corrected)f(and)g(enlar)o(ged)g(edition,)212 2159 y(San)j(Die)o(go:)g(Academic,)h(1980)62 2247 y(28.)50 b(Hess,)29 b(H.,)f(Schrader)m(,)i(R.,)f(Uhlenbrock,)g(D.A.:)f (Domination)i(of)e(semigroups)h(and)h(generalization)h(of)d(Kato')l(s) 212 2336 y(inequality)-5 b(.)20 b(Duk)o(e)g(Math.)g(J.)g Fe(44)p FC(,)g(893\226904)f(\(1977\))62 2424 y(29.)50 b(Hupfer)m(,)21 b(T)-6 b(.,)22 b(Leschk)o(e,)i(H.,)e(M\374ller)m(,)h(P) -9 b(.,)23 b(W)-6 b(arzel,)24 b(S.:)f(Existence)h(and)f(uniqueness)g (of)f(the)h(inte)o(grated)h(density)f(of)212 2513 y(states)e(for)e (Schr\366dinger)h(operators)g(with)g(magnetic)h(\002elds)g(and)f (unbounded)g(random)g(potentials.)h(e-print)e(math-)212 2603 y(ph/0010013)f(\(2000\).)62 2690 y(30.)50 b(Hupfer)m(,)26 b(T)-6 b(.,)28 b(Leschk)o(e,)h(H.,)e(W)-6 b(arzel,)29 b(S.:)g(Upper)e(bounds)h(on)g(the)g(density)h(of)e(states)i(of)f (single)g(Landau)h(le)n(v)o(els)212 2780 y(broadened)20 b(by)f(Gaussian)h(random)g(potentials.)h(e-print)e(math-ph/0011010)g (\(2000\))62 2867 y(31.)50 b(Kato,)19 b(T)-6 b(.:)20 b(Schr\366dinger)g(operators)g(with)f(singular)h(potentials.)h(Israel)f (J.)g(Math.)g Fe(13)p FC(,)g(135\226148)f(\(1972\))62 2954 y(32.)50 b(Kato,)18 b(T)-6 b(.:)18 b(Remarks)h(on)e (Schr\366dinger)h(operators)g(with)g(v)o(ector)h(potentials.)g(Inte)o (gral)f(Equations)g(Oper)l(.)f(Theory)h Fe(1)p FC(,)212 3044 y(103\226113)h(\(1978\))62 3131 y(33.)50 b(Kato,)22 b(T)-6 b(.,)22 b(Masuda,)g(K.:)g(T)m(rotter')l(s)f(product)h(formula)g (for)f(nonlinear)i(semigroups)f(generated)h(by)f(the)h(subdif)n(fer)n (-)212 3221 y(entials)e(of)e(con)m(v)o(e)o(x)h(functionals.)g(J.)g (Math.)g(Soc.)g(Japan)h Fe(30)p FC(,)e(169\226178)g(\(1978\))62 3308 y(34.)50 b(Kirsch,)20 b(W)-7 b(.:)20 b(Random)h(Schr\366dinger)f (operators:)h(A)f(course.)g(In:)g FB(Sc)o(hr\366ding)o(er)h(oper)o (ator)o(s)p FC(.)g(Holden,)f(H.,)g(Jensen,)212 3398 y(A.)f(\(eds.\),)g (Lecture)i(Notes)f(in)g(Physics)g Fe(345)p FC(,)f(Berlin:)i(Springer)m (,)e(1989,)g(pp.)h(264\226370)62 3485 y(35.)50 b(Kirsch,)24 b(W)-7 b(.,)24 b(Martinelli,)h(F)-6 b(.:)25 b(On)f(the)h(er)o(godic)f (properties)g(of)g(the)h(spectrum)g(of)f(general)h(random)f(operators.) h(J.)212 3575 y(Reine)20 b(Ange)n(w)-5 b(.)19 b(Math.)i Fe(334)p FC(,)e(141\226156)g(\(1982\))62 3662 y(36.)50 b(Kirsch,)22 b(W)-7 b(.,)23 b(Martinelli,)h(F)-6 b(.:)23 b(On)g(the)g(density)h(of)e(states)i(of)f(Schr\366dinger)g(operators)f (with)h(a)h(random)e(potential.)212 3752 y(J.)d(Phys.)h(A)f Fe(15)p FC(,)h(2139\2262156)f(\(1982\))62 3839 y(37.)50 b(K)o(ukushkin,)16 b(I.V)-10 b(.,)17 b(Meshk)o(o)o(v)-5 b(,)18 b(S.V)-10 b(.,)17 b(T)m(imofee)n(v)-5 b(,)19 b(V)-10 b(.B.:)17 b(T)-6 b(w)o(o-dimensional)18 b(electron)h(density)f(of)g (states)h(in)f(a)h(trans-)212 3929 y(v)o(erse)31 b(magnetic)i(\002eld.) f(So)o(v)-5 b(.)32 b(Phys.)f(Usp.)g Fe(31)p FC(,)g(511\226534)g (\(1988\))f([Russian)h(original:)h(Usp.)f(Fiz.)i(Nauk)e Fe(155)p FC(,)212 4018 y(219\226264)19 b(\(1988\)])62 4106 y(38.)50 b(Landau,)20 b(L.:)f(Diamagnetismus)i(der)f(Metalle.)h (Z.)f(Physik)g Fe(64)p FC(,)f(629\226637)g(\(1930\))g([in)g(German])62 4193 y(39.)50 b(Lieb,)20 b(E.H.,)f(Loss,)g(M.:)h FB(Analysis)p FC(.)g(Pro)o(vidence,)g(Rhode)h(Island:)f(Am.)f(Math.)h(Soc.,)h(1997)62 4280 y(40.)50 b(Lifshits,)27 b(I.M.,)g(Gredeskul,)g(S.A.,)h(P)o(astur)m (,)g(L.A.:)f FB(Intr)l(oduction)h(to)g(the)g(theory)g(of)g(disor)m(der) m(ed)h(systems)p FC(.)f(Ne)n(w)212 4370 y(Y)-9 b(ork:)19 b(W)m(ile)o(y)-5 b(,)20 b(1988)f([Russian)h(original:)g(Mosco)n(w:)g (Nauka,)g(1982])62 4457 y(41.)50 b(Lifshits,)19 b(M.A.:)g FB(Gaussian)h(r)o(andom)e(functions)p FC(.)j(Dordrecht:)e(Kluwer)m(,)g (1995)62 4544 y(42.)50 b(Lisk)o(e)n(vitch,)25 b(V)-10 b(.,)23 b(Mana)n(vi,)j(A.:)e(Dominated)g(semigroups)g(with)h(singular)f (comple)o(x)h(potentials.)g(J.)g(Funct.)g(Anal.)212 4634 y Fe(151)p FC(,)19 b(281\226305)g(\(1997\))62 4721 y(43.)50 b(Matsumoto,)21 b(H.:)g(On)g(the)h(inte)o(grated)g(density)f(of)g (states)h(for)f(the)g(Schr\366dinger)h(operators)f(with)g(certain)h (random)212 4811 y(electromagnetic)g(potentials.)f(J.)f(Math.)g(Soc.)g (Japan)h Fe(45)p FC(,)e(197\226214)g(\(1993\))62 4898 y(44.)50 b(Mohamed,)30 b(A.,)g(Raik)o(o)o(v)-5 b(,)31 b(G.D.:)f(On)g(the)h(spectral)g(theory)g(of)f(the)h(Schr\366dinger)f (operator)g(with)h(electromag-)212 4988 y(netic)24 b(potential.)h(In:)e FB(Pseudo-dif)o(fer)m(ential)i(calculus)f(and)f(mathematical)h(physics) p FC(.)h(Demuth,)e(M.,)h(Schrohe,)g(E.,)212 5077 y(Schulze,)d(B.-W)-7 b(.\(eds.\),)19 b(Berlin:)h(Akademie,)h(1994,)e(pp.)h(298\226390)62 5165 y(45.)50 b(Nakamura,)21 b(S.:)h(A)f(remark)g(on)g(the)g (Dirichlet-Neumann)h(decoupling)f(and)h(the)g(inte)o(grated)g(density)f (of)g(states.)i(J.)212 5254 y(Funct.)d(Anal.)g Fe(179)p FC(,)f(136\226152)g(\(2001\))62 5342 y(46.)50 b(Nakao,)26 b(S.:)h(On)e(the)i(spectral)g(distrib)n(ution)f(of)g(the)h (Schr\366dinger)f(operator)g(with)g(random)f(potential.)j(Japan.)f(J.) 212 5431 y(Math.)20 b Fe(3)p FC(,)f(111\226139)g(\(1977\))62 5518 y(47.)50 b(P)o(astur)m(,)16 b(L.:)g(On)f(the)i(Schr\366dinger)e (equation)i(with)f(a)h(random)e(potential.)j(Theor)l(.)d(Math.)h(Phys.) g Fe(6)p FC(,)g(299\226306)f(\(1971\))212 5608 y([Russian)20 b(original:)g(T)-6 b(eor)l(.)19 b(Mat.)h(Fiz.)h Fe(6)p FC(,)f(415\226424)f(\(1971\)])62 5695 y(48.)50 b(P)o(astur)m(,)21 b(L.:)g(Spectral)h(properties)f(of)g(disordered)g(systems)h(in)f(the)h (one-body)e(approximation.)h(Commun.)g(Math.)212 5785 y(Phys.)e Fe(75)p FC(,)h(179\226196)f(\(1980\))p eop %%Page: 26 26 26 25 bop 0 20 a FC(26)1994 b(T)-6 b(.)20 b(Hupfer)m(,)e(H.)i(Leschk)o (e,)g(P)-9 b(.)21 b(M\374ller)m(,)e(S.)i(W)-6 b(arzel)62 298 y(49.)50 b(P)o(astur)m(,)19 b(L.,)h(Figotin,)g(A.:)g FB(Spectr)o(a)g(of)g(r)o(andom)f(and)g(almost-periodic)h(oper)o(ator)o (s)p FC(.)g(Berlin:)h(Springer)m(,)e(1992)62 388 y(50.)50 b(Perelmuter)m(,)26 b(M.A.,)f(Semeno)o(v)-5 b(,)26 b(Y)-9 b(u.A.:)25 b(On)g(decoupling)i(of)e(\002nite)h(singularities)h(in)f (the)g(scattering)h(theory)f(for)212 478 y(the)20 b(Schr\366dinger)g (operator)f(with)h(a)g(magnetic)h(\002eld.)g(J.)f(Math.)g(Phys.)g Fe(22)p FC(,)f(521\226533)g(\(1981\))62 567 y(51.)50 b(Reed,)25 b(M.,)g(Simon,)g(B.:)h FB(Methods)f(of)g(modern)g (mathematical)g(physics)h(I:)e(Functional)h(analysis)p FC(.)g(Re)n(vised)h(and)212 657 y(enlar)o(ged)20 b(edition,)g(San)g (Die)o(go:)g(Academic,)h(1980)62 747 y(52.)50 b(Reed,)22 b(M.,)f(Simon,)h(B.:)g FB(Methods)g(of)g(modern)f(mathematical)g (physics)i(II:)d(F)-8 b(ourier)21 b(analysis,)h(self-adjointness)p FC(.)212 836 y(Ne)n(w)d(Y)-9 b(ork:)19 b(Academic,)i(1975)62 926 y(53.)50 b(Reed,)22 b(M.,)f(Simon,)g(B.:)g FB(Methods)h(of)g (modern)e(mathematical)i(physics)g(IV)-5 b(:)19 b(Analysis)j(of)f(oper) o(ator)o(s)p FC(.)g(Ne)n(w)g(Y)-9 b(ork:)212 1016 y(Academic,)21 b(1978)62 1105 y(54.)50 b(Shklo)o(vskii,)25 b(B.I.,)h(Efros,)e(A.L.:)i FB(Electr)l(onic)h(pr)l(operties)g(of)f(doped)g(semiconductor)o(s)p FC(.)g(Berlin:)h(Springer)m(,)e(1984)212 1195 y([Russian)20 b(original:)g(Mosco)n(w:)f(Nauka,)h(1979])62 1285 y(55.)50 b(Simon,)20 b(B.:)g(Uni)n(v)o(ersal)g(diamagnetism)h(of)e(spinless)i (Bose)f(systems.)h(Phys.)e(Re)n(v)-5 b(.)20 b(Lett.)h Fe(36)p FC(,)e(1083\2261084)g(\(1976\))62 1375 y(56.)50 b(Simon,)17 b(B.:)g(An)g(abstract)h(Kato')l(s)e(inequality)i(for)e (generators)h(of)f(positi)n(vity)i(preserving)e(semigroups.)h(Ind.)f (Math.)212 1464 y(J.)j Fe(26)p FC(,)h(1067\2261073)f(\(1977\))62 1554 y(57.)50 b(Simon,)20 b(B.:)g(Maximal)h(and)f(minimal)h (Schr\366dinger)e(forms.)g(J.)h(Operator)f(Theory)h Fe(1)p FC(,)f(37\22647)h(\(1979\))62 1644 y(58.)50 b(Simon,)20 b(B.:)g FB(Functional)g(inte)m(gr)o(ation)g(and)f(quantum)g(physics)p FC(.)i(Ne)n(w)e(Y)-9 b(ork:)20 b(Academic,)h(1979)62 1733 y(59.)50 b(Simon,)20 b(B.:)g(Kato')l(s)f(inequality)i(and)f(the)g (comparison)g(of)g(semigroups.)f(J.)h(Funct.)h(Anal.)e Fe(32)p FC(,)h(97\226101)f(\(1979\))62 1823 y(60.)50 b(Simon,)24 b(B.:)h(Schr\366dinger)f(operators)g(in)g(the)h (twenty-\002rst)f(century)-5 b(.)24 b(In:)g FB(Mathematical)i(Physics)e (2000)p FC(.)g(F)o(okas,)212 1913 y(A.,)e(Grigoryan,)f(A.,)h(Kibble,)h (T)-6 b(.,)22 b(Ze)o(garlinski,)g(B.)h(\(eds.\),)f(London:)g(Imperial)g (Colle)o(ge)i(Press,)f(2000,)f(pp.)g(283\226)212 2002 y(288)62 2092 y(61.)50 b(Stollmann,)20 b(P)-9 b(.:)21 b FB(Caught)f(by)g(disor)m(der:)f(Bound)h(states)g(in)g(r)o(andom)f (media)p FC(.)h(Boston:)g(Birkh\344user)m(,)f(2001)62 2182 y(62.)50 b(Ueki,)21 b(N.:)h(On)f(spectra)i(of)e(random)h (Schr\366dinger)f(operators)h(with)g(magnetic)h(\002elds.)f(Osaka)g(J.) g(Math.)g Fe(31)p FC(,)g(177\226)212 2272 y(187)d(\(1994\))62 2361 y(63.)50 b(V)-9 b(eseli)410 2360 y(\264)406 2361 y(c,)21 b(I.:)f(W)-6 b(e)o(gner)20 b(estimate)i(for)d(some)i (inde\002nite)g(Anderson-type)f(Schr\366dinger)g(operators.)g(e-print)f (mp_arc)212 2451 y(00-373)f(\(2000\))62 2541 y(64.)50 b(W)-6 b(ang,)18 b(W)-7 b(.-M.:)17 b(Microlocalization,)j(percolation,) f(and)f(Anderson)f(localization)j(for)d(the)h(magnetic)i (Schr\366dinger)212 2630 y(operator)f(with)h(a)g(random)g(potential.)h (J.)f(Funct.)g(Anal.)g Fe(146)p FC(,)f(1\22626)h(\(1997\))62 2720 y(65.)50 b(W)-6 b(e)o(gner)m(,)19 b(F)-6 b(.:)20 b(Bounds)g(on)f(the)i(density)f(of)f(states)i(in)f(disordered)g (systems.)g(Z.)g(Phys.)f(B)h Fe(44)p FC(,)g(9\22615)f(\(1981\))62 2810 y(66.)50 b(W)-6 b(e)o(yl,)17 b(H.:)f(Das)h(asymptotische)h(V)-9 b(erteilungsgesetz)18 b(der)f(Eigenwerte)g(linearer)h(partieller)f(Dif) n(ferentialgleichun-)212 2899 y(gen)23 b(\(mit)f(einer)i(Anwendung)d (auf)i(die)g(Theorie)g(der)g(Hohlraumstrahlung\).)e(Math.)i(Ann.)f Fe(71)p FC(,)h(441\226479)f(\(1912\))212 2989 y([in)d(German])62 3079 y(67.)50 b(Zak,)19 b(J.:)h(Magnetic)i(translation)e(group.)f (Phys.)h(Re)n(v)-5 b(.)20 b Fe(134)p FC(,)f(A1602\226A1606)f(\(1964\))0 3459 y FF(Citation)25 b(Index)0 3679 y FC([1])687 b(4)0 3769 y([2])567 b(2,)20 b(15)0 3859 y([3])408 b(17,)19 b(21\22623)0 3948 y([4])448 b(2,)19 b(13,)h(16)0 4038 y([5])448 b(2,)19 b(13,)h(16)0 4128 y([6])567 b(7,)20 b(10)0 4218 y([7])687 b(2)0 4307 y([8])567 b(7,)20 b(14)0 4397 y([9])328 b(7,)20 b(17,)f(19,)h(22)0 4487 y([10])328 b(2,)20 b(3,)f(5,)h(6,)g(9)0 4576 y([11])447 b(2,)20 b(8\22610)0 4666 y([12])288 b(2,)20 b(13,)f(16,)h(17)0 4756 y([13])647 b(9)0 4845 y([14])607 b(20)0 4935 y([15])647 b(8)0 5025 y([16])487 b(21,)20 b(23)0 5115 y([17])487 b(21,)20 b(22)0 5204 y([18])647 b(8)0 5294 y([19])g(7)0 5384 y([20])527 b(8,)20 b(16)0 5473 y([21])607 b(10)0 5563 y([22])647 b(4)0 5653 y([23])208 b(2,)20 b(8\22610,)f(13,)h(14) 1319 3679 y([24])368 b(2,)19 b(6,)h(9,)g(14)1319 3769 y([25])607 b(15)1319 3859 y([26])g(22)1319 3948 y([27])487 b(15,)20 b(23)1319 4038 y([28])607 b(21)1319 4128 y([29])487 b(4,)20 b(7,)g(8)1319 4218 y([30])487 b(14,)20 b(17)1319 4307 y([31])487 b(17,)20 b(21)1319 4397 y([32])487 b(17,)20 b(21)1319 4487 y([33])607 b(22)1319 4576 y([34])567 b(2,)20 b(6)1319 4666 y([35])647 b(5)1319 4756 y([36])288 b(7,)20 b(11,)f(17,)h(24)1319 4845 y([37])527 b(2,)20 b(15)1319 4935 y([38])607 b(15)1319 5025 y([39])487 b(18,)20 b(22)1319 5115 y([40])647 b(2)1319 5204 y([41])g(4)1319 5294 y([42])248 b(17,)20 b(19,)f(21,)h(22)1319 5384 y([43])527 b(7,)20 b(14)1319 5473 y([44])647 b(6)1319 5563 y([45])407 b(7,)20 b(15,)g(20)1319 5653 y([46])647 b(7)2638 3679 y([47])g(7)2638 3778 y([48])g(8)2638 3877 y([49])407 b(2,)20 b(3,)g(6\2269)2638 3975 y([50])487 b(21,)20 b(22)2638 4074 y([51])168 b(4,)20 b(11,)g(15,)f(18,)h(23)2638 4173 y([52])368 b(17,)19 b(19\22621)2638 4271 y([53])248 b(11,)20 b(19,)f(20,)h(23)2638 4370 y([54])647 b(2)2638 4469 y([55])607 b(23)2638 4567 y([56])g(21)2638 4666 y([57])368 b(17,)19 b(19,)h(21)2638 4765 y([58])407 b(7,)20 b(22,)g(23)2638 4863 y([59])487 b(18,)20 b(21)2638 4962 y([60])647 b(8)2638 5061 y([61])567 b(2,)20 b(9)2638 5159 y([62])447 b(6,)20 b(7,)g(14)2638 5258 y([63])607 b(12)2638 5357 y([64])407 b(2,)20 b(13,)g(17)2638 5455 y([65])567 b(2,)20 b(8)2638 5554 y([66])607 b(14)2638 5653 y([67])647 b(6)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0106211149626--