Content-Type: multipart/mixed; boundary="-------------0405050434445" This is a multi-part message in MIME format. ---------------0405050434445 Content-Type: text/plain; name="04-145.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-145.keywords" Dirac operators, magnetic field, conjugate operator, perturbation theory, limiting absorption principle ---------------0405050434445 Content-Type: application/postscript; name="Dirac.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Dirac.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86f Copyright 2001 Radical Eye Software %%Title: Dirac.dvi %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Bold Times-Roman Times-Italic %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o Dirac.ps Dirac.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.05.05:1104 %%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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b(Equ.)180 4479 y(Oper)-5 b(.)20 b(Theory)e Fq(34)i FC(\(1999\),)e(377\226395.)42 4645 y([3])40 b(P)-9 b(.)20 b(Briet)h(and)f(H.D.)g(Cornean,)f Ft(Locating)g(the)h(spectrum)g(for)h (ma)o(gnetic)e(Sc)o(hr)2455 4646 y(\250)2448 4645 y(oding)o(er)f(and)h (Dir)o(ac)i(oper)o(ator)o(s)p FC(,)180 4745 y(Comm.)e(P)o(artial)i(Dif) n(ferential)e(Equations)f Fq(27)i FC(\(2002\),)e(no.)i(5-6,)f (1079\2261101.)1671 5059 y(11)p eop %%Page: 12 12 12 11 bop 42 523 a FC([4])40 b(A.M.)15 b(Boutet)g(de)h(Mon)m(v)o(el)e (and)g(R.)j(Purice,)d Ft(A)i(distinguished)e(self-adjoint)g(e)n (xtension)h(for)h(the)f(Dir)o(ac)h(oper)o(ator)180 623 y(with)29 b(str)l(ong)f(local)g(singularities)g(and)f(arbitr)o(ary)h (behaviour)f(at)h(in\002nity)p FC(,)f(Rep.)i(Math.)f(Phys.)f Fq(34)h FC(\(1994\),)180 722 y(no.)19 b(3,)h(351\226360.)42 888 y([5])40 b(P)-9 b(.R.)16 b(Chernof)n(f,)d Ft(Sc)o(hr)823 889 y(\250)816 888 y(oding)o(er)h(and)g(Dir)o(ac)i(oper)o(ator)o(s)e (with)j(singular)d(potentials)h(and)f(hyperbolic)h(equations)p FC(,)180 988 y(P)o(aci\002c)20 b(J.)h(Math.)f Fq(72)g FC(\(1977\),)e(no.)h(2,)h(361\226382.)42 1154 y([6])40 b(T)-6 b(.R.)20 b(Cho)n(w)-5 b(,)19 b Ft(A)h(spectr)o(al)f(theory)h (for)g(dir)m(ect)g(inte)m(gr)o(als)f(of)h(oper)o(ator)o(s)p FC(,)e(Math.)i(Ann.)f(Phys.)g Fq(188)g FC(\(1970\),)e(285\226)180 1254 y(303.)42 1420 y([7])40 b(L.I.)24 b(Danilo)o(v)-5 b(,)23 b Ft(On)i(the)g(spectrum)g(of)g(the)g(two-dimensional)e (periodic)h(Dir)o(ac)h(oper)o(ator)p FC(,)e(Theo.)h(and)g(Math.)180 1519 y(Physics)c Fq(118)f FC(\(1999\),)f(no.)i(1,)g(1\22611.)42 1685 y([8])40 b(V)-11 b(.)20 b(Geor)o(gescu)e(and)h(C.)h(G)5 b(\264)-33 b(erard,)18 b Ft(On)i(the)g(V)-6 b(irial)19 b(theor)m(em)h(in)f(quantum)f(mec)o(hanics)p FC(,)g(Commun.)g(Math.)h (Phys.)180 1785 y Fq(208)g FC(\(1999\),)f(275\226281.)42 1951 y([9])40 b(V)-11 b(.)30 b(Geor)o(gescu)e(and)h(M.)h(M)5 b(\020)-33 b(antoiu,)29 b Ft(On)h(the)g(spectr)o(al)f(theory)h(of)g (singular)f(Dir)o(ac)h(type)g(Hamiltonians)p FC(,)e(J.)180 2051 y(Operator)19 b(Theory)f Fq(46)i FC(\(2001\),)e(289\226321.)0 2217 y([10])40 b(A.)20 b(Grigis)f(and)g(A.)h(Mohamed,)e Ft(F)l(initude)g(des)i(lacunes)f(dans)g(le)h(spectr)m(e)g(de)f(l'op) 2580 2218 y(\264)2576 2217 y(er)o(ateur)f(de)i(Sc)o(hr)3096 2218 y(\250)3089 2217 y(oding)o(er)d(et)180 2316 y(de)22 b(celui)h(de)f(Dir)o(ac)h(avec)f(des)h(potentiels)1443 2317 y(\264)1438 2316 y(electrique)f(et)h(ma)o(gn)2065 2317 y(\264)2061 2316 y(etique)e(p)2332 2317 y(\264)2328 2316 y(eriodiques)p FC(,)g(J.)i(Math.)f(K)n(yoto)g(Uni)n(v)-5 b(.)180 2416 y Fq(33)20 b FC(\(1993\),)d(no.)j(4,)g(1071\2261096.)0 2582 y([11])40 b(B.)18 b(Helf)n(fer)m(,)e(J.)i(Nourrigat)d(and)i(X.P)-9 b(.)18 b(W)-7 b(ang,)17 b Ft(Sur)g(le)h(spectr)m(e)g(de)f(l')2100 2583 y(\264)2096 2582 y(equation)f(de)h(Dir)o(ac)h(\(dans)e FA(R)2968 2552 y FB(2)3029 2582 y Ft(ou)h FA(R)3184 2552 y FB(3)3227 2582 y Ft(\))h(avec)180 2682 y(c)o(hamp)h(ma)o(gn)610 2683 y(\264)606 2682 y(etique)p FC(,)f(Ann.)h(scient.)1280 2664 y(\264)1268 2682 y(Ec.)i(Norm.)e(Sup.)g Fq(22)h FC(\(1989\),)e(515\226533.)0 2848 y([12])40 b(M.)19 b(M)5 b(\020)-33 b(antoiu)18 b(and)g(M.)h(P)o(ascu,)g Ft(P)-7 b(erturbations)18 b(of)h(ma)o(gnetic)f(Sc)o(hr)2121 2849 y(\250)2114 2848 y(oding)o(er)f(oper)o(ator)o(s)p FC(,)h(Lett.)h(Math.) g(Phys.)f Fq(54)180 2947 y FC(\(2000\),)g(181\226192.)0 3113 y([13])40 b(E.)21 b(Mourre,)e Ft(Absence)h(of)h(singular)f (continuous)f(spectrum)i(for)g(certain)g(self-adjoint)e(oper)o(ator)o (s)p FC(,)h(Commun.)180 3213 y(Math.)g(Phys.)f Fq(78)h FC(\(1981\),)e(391\226408.)0 3379 y([14])40 b(M.)21 b(Reed)g(and)f(B.)h (Simon,)f Ft(Methods)g(of)h(modern)f(mathematical)f(physics,)i(II)f(&)h (IV)p FC(,)f(Academic)g(Press,)i(Ne)n(w)180 3479 y(Y)-9 b(ork,)19 b(1972\2261978.)0 3645 y([15])40 b(B.)21 b(Thaller)m(,)e Ft(The)h(Dir)o(ac)g(Equation)p FC(,)e(Springer)n(-V)-9 b(erlag,)17 b(1992.)0 3811 y([16])40 b(K.)22 b(Y)-9 b(ok)o(o)o(yama,)21 b Ft(Limiting)h(absorption)f(principle)h(for)g(Dir)o(ac)h(oper)o(ator)e (with)i(constant)e(ma)o(gnetic)h(\002eld)g(and)180 3910 y(long-r)o(ang)o(e)17 b(potential)p FC(,)i(Osaka)h(J.)h(Math.)f Fq(38)g FC(\(2001\),)e(649\226666.)1671 5059 y(12)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0405050434445--