Content-Type: multipart/mixed; boundary="-------------0308211448744" This is a multi-part message in MIME format. ---------------0308211448744 Content-Type: text/plain; name="03-378.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-378.keywords" Jacobi matrices, Spectral theory ---------------0308211448744 Content-Type: application/postscript; name="jns1rev.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="jns1rev.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: jns1rev.dvi %%CreationDate: Thu Aug 21 14:45:21 2003 %%Pages: 13 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMR10 CMTI10 CMBX10 CMMI10 CMMI8 CMSY10 %%+ CMBX12 CMMI12 CMR8 MSBM10 CMSY8 CMEX10 CMTI12 CMR6 CMMI6 CMSY6 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf jns1rev %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2003.08.21:1444 %%BeginProcSet: tex.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/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]{Ci}imagemask restore}B/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: alt-rule.pro %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 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 174 /alpha put dup 177 /delta put dup 180 /eta put dup 184 /lambda put dup 190 /sigma put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 111 /o put dup 115 /s put dup 117 /u put dup 119 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 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 161 /minus put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 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 174 /alpha put dup 84 /T put dup 108 /l put dup 115 /s put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 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 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 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 174 /ff put dup 175 /fi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 65 /A put dup 68 /D put dup 69 /E put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 83 /S put dup 84 /T put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 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 161 /parenleftbig put dup 162 /parenrightbig put dup 163 /bracketleftbig put dup 164 /bracketrightbig put dup 169 /braceleftbig put dup 170 /bracerightbig put dup 175 /vextendsingle put dup 176 /vextenddouble put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 183 /bracketleftbigg put dup 184 /bracketrightbigg put dup 189 /braceleftbigg put dup 190 /bracerightbigg put dup 195 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 80 /summationtext put dup 81 /producttext put dup 83 /uniontext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 101 /tildewide put dup 104 /bracketleftBig put dup 105 /bracketrightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CAC6A7BEB5D02276E511FFAF2AE11910 DE076F24311D94D07CACC323F360887F1EA11BDDA7927FF3325986FDB0ABDFC8 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 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 161 /minus put dup 164 /asteriskmath put dup 184 /greaterequal put dup 49 /infinity put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 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 78 /N put dup 82 /R put dup 114 /integerdivide put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 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 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 61 /equal put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 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 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 58 /colon put dup 65 /A put dup 67 /C put dup 69 /E put dup 73 /I put dup 75 /K put dup 79 /O put dup 80 /P put dup 82 /R put dup 84 /T put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 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 162 /Delta put dup 174 /ff put dup 175 /fi put dup 177 /ffi put dup 182 /acute put dup 33 /exclam put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 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 174 /alpha put dup 184 /lambda put dup 60 /less put dup 61 /slash put dup 99 /c put dup 110 /n put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 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 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 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B30E20BEE58CA400C9E8F89E875D6B2B358A6C916BE058F33D363537E1243FF3 11F1BDB339D9413911FABEFDDA7CA25C7B769360B335953B1186EE2430243F1B 511B6B1F4016A98F4E56E58F7F0F6B945C59AE0FFA3706A4BC08B9905BB78E70 0DDA17F6BC111D17A1883E5F47846B37075745C761F5CB638C7871B2ACD35FDB 004738456B5FEF221F047117E1102EDA7714040C1A1C489F09D31F312438414A 87BB04D6149166DA0C8718D00C3D7C9B8BBF0CB99DDB32C4B1F7F62F2D9D97EA A248CF577B9A47EE40028B51D637AD 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 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 48 /zero put dup 56 /eight put dup 68 /D put dup 69 /E put dup 78 /N put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 118 /v put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 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 174 /ff put dup 175 /fi put dup 39 /quoteright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put dup 122 /z put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 8000 8000 (jns1rev.dvi) @start /Fa 194[1377 10[877 50[{}2 1912.83 /CMR17 rf /Fb 171[1098 84[{}1 1912.83 /CMMI12 rf /Fc 255[640{}1 664.176 /CMSY6 rf /Fd 140[388 6[267 23[486 72[534 11[{}4 664.176 /CMMI6 rf /Fe 205[406 406 406 48[{}3 664.176 /CMR6 rf /Ff 132[664 531 631 598 863 598 697 432 531 548 598 664 664 731 1063 332 598 399 399 664 598 399 598 664 598 598 664 3[399 1[399 3[1298 2[930 731 2[881 996 966 1165 815 1[682 501 3[881 981 2[966 15[664 2[399 465 399 2[531 531 27[731 797 11[{}50 1328.35 /CMTI12 rf /Fg 150[627 627 2[738 11[1697 1919 4[1107 1[1255 1402 14[1162 1162 10[886 886 886 886 1162 1162 6[1070 1070 4[775 775 1052 1052 4[996 996 4[701 701 978 978 793 793 2[738 443 2[775 775 4[553 553 609 609{}38 1328.35 /CMEX10 rf /Fh 148[664 369 2[664 664 47[0 3[886 1328 15[1328 8[1033 2[1033 1033 13[1033 3[1033 369 1033{}15 1328.35 /CMSY10 rf /Fi 149[261 56[941 27[732 17[470 2[732{}5 885.568 /CMSY8 rf /Fj 141[1033 31[959 3[959 78[{}3 1328.35 /MSBM10 rf /Fk 194[732 8[470 470 470 470 470 4[732 43[{}7 885.568 /CMR8 rf /Fl 133[604 1[739 930 1[740 1[613 3[625 776 1[387 676 538 3[641 603 676 560 553 683 9[1228 1[883 762 800 3[994 1042 1258 885 1[719 574 3[963 1080 931 988 975 2[1012 650 1012 361 361 18[852 4[609 6[739 5[759 3[642 2[576 2[827 11[{}43 1328.35 /CMMI12 rf /Fm 137[1136 1196 837 849 879 2[1076 1196 1793 598 2[598 2[658 982 1196 956 1[1046 14[1605 1[1470 1616 5[801 3[1412 1[1554 13[1076 1076 1076 1076 1076 49[{}26 1912.83 /CMBX12 rf /Fn 132[650 578 686 686 939 686 723 506 513 506 686 723 650 723 1084 361 686 397 361 723 650 397 578 723 578 723 650 3[361 650 361 1[975 1[1336 975 975 939 723 957 1[885 1012 975 1192 813 1011 668 469 975 1021 849 885 993 939 921 975 3[1012 2[361 650 650 650 650 650 650 650 650 650 650 1[361 434 361 1012 1[506 506 361 4[650 361 13[650 4[1084 1[723 759 9[1084 1[{}79 1328.35 /CMR12 rf /Fo 134[789 1[1079 2[581 589 610 2[747 830 1245 415 789 2[830 747 457 682 830 664 1[726 12[1039 1[1115 1[1021 4[1170 9[1128 6[415 4[747 747 747 747 747 2[415 46[{}29 1328.35 /CMBX12 rf /Fp 235[943 20[{}1 1212.12 /CMSY10 rf /Fq 140[435 2[474 455 571 1[281 490 381 4[436 3[500 12[548 5[747 1[640 14[470 49[604 11[{}14 885.568 /CMMI8 rf /Fr 145[728 10[525 37[606 943 38[707 9[775 11[{}6 1212.12 /CMMI10 rf /Fs 139[542 550 574 14[620 774 678 31[1054 65[{}7 1212.12 /CMBX10 rf /Ft 134[589 2[558 1[403 496 511 2[620 681 4[372 620 1[372 558 620 558 558 620 18[901 8[822 915 11[620 7[620 48[{}20 1212.12 /CMTI10 rf /Fu 133[539 640 1[875 640 673 471 478 475 640 673 606 673 1010 337 640 1[337 673 606 370 539 673 539 673 606 9[1246 1[909 875 673 892 1[825 2[1111 758 943 623 438 909 3[926 875 859 909 3[943 3[606 606 606 1[606 606 606 606 606 606 1[337 404 337 943 3[337 26[673 707 11[{}57 1212.12 /CMR10 rf /Fv 133[694 4[867 607 616 607 2[780 867 1[434 824 1[434 1[780 1[694 2[867 780 13[867 4[1170 3[802 2[1225 71[{}18 1594.02 /CMR12 rf /Fw 134[1113 3[1173 813 825 813 1[1173 1053 1173 1773 573 2[573 1173 1[633 933 1173 933 1173 1053 13[1173 8[1082 15[573 58[{}21 2295.84 /CMR17 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 8000dpi TeXDict begin %%BeginPaperSize: a4 a4 %%EndPaperSize end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 2711 7643 a Fw(Sp)60 b(ectral)692 b(theory)h(for)g(a)g(class)g(of)g(p)60 b(erio)g(dically)693 b(p)60 b(erturb)g(ed)3849 10411 y(un)-60 b(b)60 b(ounded)692 b(Jacobi)h(matrices:)933 b(elemen)-60 b(tary)692 b(metho)60 b(ds)23049 14354 y Fv(Jan)521 b(Janas)12428 18339 y Fu(Insitute)405 b(of)f(Mathematics,)h(P)-34 b(olish)404 b(Academ)-34 b(y)404 b(of)h(Sciences)14874 20332 y(ul.)f(sw.)g(T)-101 b(omasza)405 b(30,)f(31-027)g(Krak)-34 b(o)g(w,)404 b(P)-34 b(oland)21124 24317 y Fv(Serguei)520 b(Nab)43 b(ok)-43 b(o)11295 28302 y Fu(Departmen)-34 b(t)405 b(of)g(Mathematical)f(Ph)-34 b(ysics,)404 b(Insitute)h(of)f(Ph)-34 b(ysics)15814 30294 y(St.)404 b(P)-34 b(etersburg)405 b(Univ)-34 b(ersit)g(y)-101 b(,)403 b(Uliano)-34 b(vk)-67 b(aia)404 b(1)14851 32287 y(198904)g(St.)h(P)-34 b(etergo\256,)403 b(St.)i(P)-34 b(etersburg,)404 b(Russia)22094 36272 y Fv(Gun)-43 b(ter)520 b(Stolz)8381 40257 y Fu(Departmen)-34 b(t)405 b(of)g(Mathematics,)f (Univ)-34 b(ersit)g(y)404 b(of)h(Alabama)f(at)h(Birmingham)14839 42250 y(CH)f(452,)g(Birmingham,)g(AL)g(35294-1170,)g(USA)9587 46235 y Ft(De)-62 b(dic)g(ate)g(d)431 b(to)i(Norrie)g(Everitt)f(on)i (the)e(o)-62 b(c)g(c)g(asion)431 b(of)i(his)g(80th)f(birthday)23790 51175 y Fs(Abstract)4755 53422 y Fu(W)-101 b(e)459 b(use)g(elemen)-34 b(tary)459 b(metho)34 b(ds)460 b(to)g(giv)-34 b(e)459 b(a)g(full)h(c)-34 b(haracterization)459 b(of)g(the)h(sp)34 b(ectral)459 b(prop)34 b(erties)2937 54928 y(of)569 b(un)-34 b(b)34 b(ounded)572 b(Jacobi)d(matrices)g(with)h(zero)f(diagonal)h(and) g(o\256-diagonal)g(en)-34 b(tries)569 b(of)h(the)f(t)-34 b(yp)34 b(e)2937 56433 y Fr(\270)3644 56615 y Fq(n)4857 56433 y Fu(=)587 b Fr(n)7115 55993 y Fq(\256)8144 56433 y Fu(+)369 b Fr(c)9981 56615 y Fq(n)10607 56433 y Fu(,)592 b(where)554 b(1)p Fr(=)p Fu(2)588 b Fr(<)f(\256)592 b Fp(\267)587 b Fu(1)554 b(and)i Fr(c)26217 56615 y Fq(n)27397 56433 y Fu(is)e(a)g(real)g(p)34 b(erio)g(dic)553 b(sequence.)989 b(The)555 b(sp)34 b(ectral)2937 57939 y(prop)g(erties)587 b(dep)34 b(end)588 b(strongly)g(on)g(the)h(parit)-34 b(y)588 b(of)g(the)g(minimal)f(p)34 b(erio)g(d)587 b(of)h Fr(c)40764 58121 y Fq(n)41390 57939 y Fu(.)1090 b(The)588 b(metho)34 b(ds)2937 59444 y(used)440 b(are)g(asymptotic)h (diagonalization)f(tec)-34 b(hniques,)450 b(including)441 b(the)f(\257nite)h(di\256erence)e(v)-34 b(ersion)440 b(of)2937 60950 y(Levinson's)403 b(theorem,)h(sub)34 b(ordinacy)405 b(theory)-101 b(,)403 b(and)i(the)g(v)-67 b(ariational)403 b(principle.)-315 65458 y Fo(Keyw)-42 b(ords:)580 b Fn(Jacobi)434 b(Matrices,)g(Sp)36 b(ectral)434 b(Theory)26132 74188 y(1)p eop end %%Page: 2 2 TeXDict begin 2 1 bop -315 2274 a Fm(1)2152 b(In)-60 b(tro)60 b(duction)-315 5195 y 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Fn(and)433 b Fl(s)8648 4079 y Fk(0)9607 3880 y Fn(su\261cien)-36 b(tly)433 b(large\))11055 5422 y Fg(\260)11055 6219 y(\260)11055 7016 y(\260)11055 7813 y(\260)11055 8610 y(\260)12470 6087 y Fq(n)11906 6485 y Fg(Y)11793 9314 y Fq(k)24 b Fk(=)p Fq(T)13938 7747 y Fl(B)67 b Fn(\()p Fl(k)45 b Fn(\))16726 5422 y Fg(\260)16726 6219 y(\260)16726 7016 y(\260)16726 7813 y(\260)16726 8610 y(\260)17464 5773 y Fk(2)19108 7747 y Fn(=)21237 5422 y Fg(\260)21237 6219 y(\260)21237 7016 y(\260)21237 7813 y(\260)21237 8610 y(\260)21975 7747 y Fl(B)67 b Fn(\()p Fl(n)p Fn(\))221 b Fl(:)g(:)g(:)j(B)67 b Fn(\()p Fl(N)139 b(T)181 b Fn(\))31200 6087 y Fq(N)94 b Fi(\241)p Fk(1)31372 6485 y Fg(Y)31402 9275 y Fq(s)p Fk(=1)33464 7747 y Fl(C)h Fn(\()p Fl(s)p Fn(\))36115 5422 y Fg(\260)36115 6219 y(\260)36115 7016 y(\260)36115 7813 y(\260)36115 8610 y(\260)36852 5699 y Fk(2)19097 12508 y Fh(\267)1107 b Fl(M)22495 12707 y Fk(2)23243 10184 y Fg(\260)23243 10981 y(\260)23243 11778 y(\260)23243 12575 y(\260)23243 13372 y(\260)23981 10848 y Fq(N)94 b Fi(\241)p Fk(1)24154 11246 y Fg(Y)24184 14036 y Fq(s)p Fk(=1)26245 12508 y Fl(C)h Fn(\()p Fl(s)p Fn(\))28896 10184 y Fg(\260)28896 10981 y(\260)28896 11778 y(\260)28896 12575 y(\260)28896 13372 y(\260)29634 10460 y Fk(2)30528 12508 y Fh(\267)370 b Fl(M)33189 12707 y Fk(3)33946 10848 y Fq(N)94 b Fi(\241)p Fk(1)34119 11246 y Fg(Y)33936 14036 y Fq(s)p Fk(=)p Fq(s)35538 14159 y Fe(0)36221 12508 y Fh(j)p Fn(det)221 b Fl(C)95 b Fn(\()p Fl(s)p Fn(\))p Fh(j)19108 17133 y Fn(=)1117 b Fl(M)22495 17332 y Fk(3)23292 15472 y Fq(N)94 b(T)131 b Fi(\241)p Fk(1)23804 15871 y Fg(Y)23243 18700 y Fq(k)24 b Fk(=)p Fq(s)24924 18823 y Fe(0)25384 18700 y Fq(T)26284 17133 y Fh(j)p Fn(det)221 b Fl(B)67 b Fn(\()p Fl(k)45 b Fn(\))p Fh(j)19097 21573 y(\267)1107 b Fl(M)22495 21772 y Fk(4)23815 19913 y Fq(n)23252 20311 y Fg(Y)23243 23140 y Fq(k)24 b Fk(=2)25180 21573 y Fh(j)p Fn(det)221 b Fl(B)67 b Fn(\()p Fl(k)45 b Fn(\))p Fh(j)221 b Fl(;)-315 25112 y Fn(for)434 b(some)g(p)36 b(ositiv)-36 b(e)434 b(constan)-36 b(ts)434 b Fl(M)16761 25311 y Fk(2)17287 25112 y Fl(;)221 b(M)19127 25311 y Fk(3)20087 25112 y Fn(and)433 b Fl(M)23874 25311 y Fk(4)24400 25112 y Fn(.)1636 26717 y(But)543 b(det)221 b Fl(B)67 b Fn(\()p Fl(k)45 b Fn(\))556 b(=)g Fl(\270)12028 26916 y Fq(k)24 b Fi(\241)p Fk(1)13798 26717 y Fl(=\270)15207 26916 y Fq(k)16320 26717 y Fn(and)543 b(the)g(ab)36 b(o)-36 b(v)g(e)544 b(estimates)g(imply)g(that)f(for)h(an)-36 b(y)544 b(solution)581 b Fg(e)-776 b Fl(u)544 b Fn(of)g(\(2.2\),)-315 28322 y Fh(k)37 b Fg(e)-775 b Fl(u)p Fn(\()p Fl(n)p Fn(\))p Fh(k)3541 27840 y Fk(2)4581 28322 y Fh(\267)514 b Fn(const)222 b Fl(\270)10079 27840 y Fi(\241)p Fk(1)10079 28651 y Fq(n)11336 28322 y Fn(.)834 b(Using)519 b(the)f(generalized)h(Behnc)-36 b(k)g(e-Stolz)518 b(Lemma,)540 b(see)519 b([JN1)q(],)540 b(it)519 b(follo)-36 b(ws)521 b(that)-315 29927 y(\(2.1\))421 b(has)f(no)g(sub)36 b(ordinate)420 b(solutions.)574 b(Finally)-108 b(,)424 b(b)-36 b(y)420 b(applying)h(Gilb)36 b(ert-Kahn-P)-36 b(earson)419 b(theory)h([KP])h(w)-36 b(e)-315 31532 y(conclude)433 b(that)g Fl(J)557 b Fn(is)434 b(purely)f(absolutely)h(con)-36 b(tin)g(uous)433 b(in)g Fj(R)p Fn(.)579 b(The)434 b(pro)36 b(of)434 b(of)g(Theorem)g(1.1)g(is)g(complete.)1636 33137 y(W)-108 b(e)314 b(emphasize)f(that)g(in)h(the)f(o)36 b(dd)313 b(case)i(the)e(analysis)i(is)f(simple)g(b)36 b(ecause)313 b(the)g(matrices)h Fl(E)78 b Fn(\()p Fl(n)p Fn(\))314 b(are)f(small)-315 34743 y(real)382 b(p)36 b(erturbations)380 b(of)h(the)g(real)h(matrix)f Fl(E)459 b Fn(with)381 b(elliptic)h(sp)36 b(ectrum)380 b(\(complex)i(conjugate)f (eigen)-36 b(v)-72 b(alues\).)-315 36348 y(Hence)317 b(the)g(sp)36 b(ectrum)316 b(of)i Fl(E)78 b Fn(\()p Fl(n)p Fn(\))317 b(is)h(again)g(elliptic)g(and)f(this)g(leads)g(to)h(the)e (conclusion)i(ab)36 b(out)317 b(pure)f(absolute)-315 37953 y(con)-36 b(tin)g(uit)g(y)433 b(of)h(the)f(sp)36 b(ectrum)433 b(of)h Fl(J)123 b Fn(.)-315 42313 y Fm(4)2152 b(Ev)-60 b(en)717 b(case)-315 45233 y Fo(Pro)42 b(of)641 b(of)g(Theorem)i(1.2.)953 b Fn(If)559 b(the)f(minimal)h(p)36 b(erio)g(d)558 b Fl(T)739 b Fn(is)559 b(ev)-36 b(en,)590 b(i.e.)953 b Fl(T)762 b Fn(=)581 b(2)p Fl(L)p Fn(,)590 b(then)557 b(the)h(sp)36 b(ectral)-315 46838 y(structure)364 b(of)i Fl(J)488 b Fn(is)365 b(more)g(complicated.)556 b(Again,)380 b(let)365 b Fl(\270)g Fn(b)36 b(e)365 b(real.)556 b(By)366 b(rep)36 b(eating)365 b(the)f(computation)h(in)g(pairs)-315 48443 y(of)434 b(transfer)g(matrices)g(w)-36 b(e)434 b(ha)-36 b(v)g(e)8119 51759 y Fl(C)95 b Fn(\()p Fl(n)p Fn(\))1107 b(:=)14519 50098 y Fq(T)131 b Fi(\241)p Fk(1)14611 50497 y Fg(Y)14641 53286 y Fq(s)p Fk(=0)16622 51759 y Fl(B)67 b Fn(\()p Fl(nT)476 b Fn(+)295 b Fl(s)p Fn(\))12220 55246 y(=)1287 b(\()p Fh(\241)p Fn(1\))17214 54697 y Fq(L)18131 54170 y Fg(\241)18740 55246 y Fn(1)296 b Fh(\241)f Fl(\256)8 b Fn(\()p Fl(nT)181 b Fn(\))24580 54697 y Fi(\241)p Fk(1)25838 54170 y Fg(\242)26447 54467 y Fq(L)14519 56891 y(L)p Fi(\241)p Fk(1)14592 57290 y Fg(Y)14624 60089 y Fq(j)51 b Fk(=0)16362 56679 y Fg(\267)17063 58552 y Fl(I)399 b Fh(\241)295 b Fn(\()p Fl(nT)181 b Fn(\))22095 58003 y Fi(\241)p Fq(\256)23487 56679 y Fg(\265)24243 57738 y Fl(c)24803 57937 y Fk(2)p Fq(j)26056 57738 y Fh(\241)295 b Fl(c)27944 57937 y Fk(2)p Fq(j)51 b Fi(\241)p Fk(1)33208 57738 y Fl(\270)26388 59343 y Fh(\241)p Fl(\270)2588 b(c)31328 59542 y Fk(2)p Fq(j)51 b Fk(+1)33782 59343 y Fh(\241)296 b Fl(c)35671 59542 y Fk(2)p Fq(j)36406 56679 y Fg(\266)37458 58552 y Fn(+)f Fl(O)40016 57476 y Fg(\241)40625 58552 y Fl(n)41401 58003 y Fi(\241)p Fk(2)p Fq(\256)43263 57476 y Fg(\242)43872 56679 y(\270)12220 62774 y Fn(=)1287 b Fl(d)15195 62973 y Fq(n)16043 60901 y Fg(\267)16744 62774 y Fl(I)399 b Fh(\241)296 b Fn(\()p Fl(nT)181 b Fn(\))21777 62226 y Fi(\241)p Fq(\256)23390 60901 y Fg(\265)24819 61960 y Fl(a)2140 b(b)24367 63566 y Fh(\241)p Fl(b)1107 b Fh(\241)p Fl(a)28776 60901 y Fg(\266)30049 62774 y Fn(+)295 b Fl(O)32608 61698 y Fg(\241)33217 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Fn(\))45777 67949 y Fk(1)p Fq(=)p Fk(2)47244 68431 y Fn(.)547 b(Pro)-36 b(vided)-315 70867 y(that)489 b Fl(a)3242 70385 y Fk(2)4100 70867 y Fh(\241)333 b Fl(b)6019 70385 y Fk(2)7034 70867 y Fn(is)489 b(di\256eren)-36 b(t)488 b(from)i(zero,)503 b(w)-36 b(e)490 b(ma)-36 b(y)489 b(diagonalize)i Fl(A)e Fn(through)f Fl(A)463 b Fn(=)h Fl(S)77 b(D)42810 71066 y Fk(1)43336 70867 y Fl(S)44213 70385 y Fi(\241)p Fk(1)45470 70867 y Fn(,)504 b(where)489 b Fl(D)51228 71066 y Fk(1)52217 70867 y Fn(=)26132 74188 y(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop -315 2274 a Fn(diag)222 b(\()p Fl(z)3401 2473 y Fk(+)4188 2274 y Fl(;)f Fh(\241)p Fl(z)6407 2473 y Fk(+)7195 2274 y Fn(\).)629 b(It)451 b(is)g(clear)g(that)f(the)g (prop)36 b(erties)450 b(of)h(generalized)g(eigen)-36 b(v)g(ectors)451 b(of)g Fl(J)574 b Fn(dep)36 b(end)449 b(strongly)-315 3880 y(on)433 b(the)h(sign)f(of)i Fl(a)8577 3398 y Fk(2)9397 3880 y Fh(\241)296 b Fl(b)11279 3398 y Fk(2)11805 3880 y Fn(.)1636 5485 y(Assume)433 b(\257rst)g(that)-315 7090 y(i\))1734 b Fl(a)2969 6608 y Fk(2)3790 7090 y Fh(\241)295 b Fl(b)5671 6608 y Fk(2)6566 7090 y Fl(<)369 b Fn(0.)1636 8695 y(Then)433 b Fl(z)5636 8894 y Fk(+)6857 8695 y Fn(is)h(pure)f (imaginary)-108 b(.)579 b(W)-108 b(e)434 b(ha)-36 b(v)g(e)7772 10719 y Fg(\260)7772 11516 y(\260)7772 12313 y(\260)7772 13110 y(\260)7772 13907 y(\260)8976 11384 y Fq(N)8548 11782 y Fg(Y)8510 14572 y Fq(n)p Fk(=1)10504 13044 y Fl(C)95 b Fn(\()p Fl(n)p Fn(\))13318 10719 y Fg(\260)13318 11516 y(\260)13318 12313 y(\260)13318 13110 y(\260)13318 13907 y(\260)14056 10996 y Fk(2)14951 13044 y Fn(=)16332 10719 y Fg(\257)16332 11516 y(\257)16332 12313 y(\257)16332 13110 y(\257)16332 13907 y(\257)17241 11384 y Fq(N)16812 11782 y Fg(Y)16774 14572 y Fq(n)p Fk(=1)18769 13044 y Fl(d)19445 13243 y Fq(n)20071 10719 y Fg(\257)20071 11516 y(\257)20071 12313 y(\257)20071 13110 y(\257)20071 13907 y(\257)20514 10996 y Fk(2)21261 10719 y Fg(\260)21261 11516 y(\260)21261 12313 y(\260)21261 13110 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y Fi(\241)p Fq(\256)32931 18656 y Fl(D)34011 18855 y Fk(1)34537 17580 y Fg(\244)222 b(\243)35865 18656 y Fl(I)399 b Fn(+)295 b Fl(O)39397 17580 y Fg(\241)40006 18656 y Fl(n)40782 18108 y Fi(\241)p Fk(2)p Fq(\256)42644 17580 y Fg(\242\244)44028 18656 y Fl(:)-315 20981 y Fn(Therefore)434 b(the)f(righ)-36 b(t)433 b(hand)g(side)h(of)g(\(4.2\))g(can)g(b)36 b(e)433 b(estimated)g(from)i(ab)36 b(o)-36 b(v)g(e)434 b(b)-36 b(y)14536 25150 y Fl(C)15467 25349 y Fk(1)16214 24075 y Fg(\241)16822 25150 y Fl(N)18003 24602 y Fi(\241)18897 24240 y Fd(\256)p 18867 24401 594 40 v 18867 24949 a(T)19649 24075 y Fg(\242)20258 24305 y Fk(2)p Fq(L)22111 23490 y(N)21683 23889 y Fg(Y)21645 26678 y Fq(n)p Fk(=1)23639 24075 y Fg(\241)24248 25150 y Fn(1)296 b(+)e Fl(O)27752 24075 y Fg(\241)28361 25150 y Fl(n)29137 24602 y Fi(\241)p Fk(2)p Fq(\256)30999 24075 y Fg(\242\242)32586 25150 y Fh(\267)369 b Fl(C)34919 25349 y Fk(2)35444 25150 y Fl(N)36625 24602 y Fi(\241)p Fq(\256)38016 25150 y Fl(;)-315 29267 y Fn(where)433 b Fl(C)4373 29466 y Fk(1)4899 29267 y Fl(;)221 b(C)6412 29466 y Fk(2)7307 29267 y Fl(>)369 b Fn(0.)578 b(This)434 b(is)g(ob)-36 b(vious)434 b(b)36 b(ecause)433 b(the)h(matrices)f(exp)q([)p Fh(\241)p Fn(\()p Fl(nT)181 b Fn(\))37634 28785 y Fi(\241)p Fq(\256)39026 29267 y Fl(D)40106 29466 y Fk(1)40631 29267 y Fn(])434 b(are)g(unitary)-108 b(.)1636 30872 y(Hence,)418 b(again)d Fh(k)37 b Fg(e)-775 b Fl(u)q Fn(\()p Fl(n)p Fn(\))p Fh(k)369 b(\267)g Fl(M)139 b(\270)17080 30390 y Fi(\241)p Fk(1)17080 31201 y Fq(n)18752 30872 y Fn(and)414 b(so)g(\(2.1\))h(has)f(no)g(sub) 36 b(ordinate)414 b(solutions.)572 b(Consequen)-36 b(tly)415 b Fl(J)537 b Fn(is)-315 32843 y(purely)433 b(absolutely)i(con)-36 b(tin)g(uous)432 b(in)i Fj(R)295 b(r)20492 31368 y Fg(h)21252 32209 y Fi(\241j)p Fq(a)p Fi(j)p 21252 32537 1755 54 v 21809 33301 a Fq(L)23139 32843 y Fl(;)23854 32209 y Fi(j)p Fq(a)p Fi(j)p 23854 32537 1023 54 v 24046 33301 a Fq(L)25010 31368 y Fg(i)25637 32843 y Fn(.)1636 34739 y(In)433 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y Fg(1)24788 41989 y(A)12046 47168 y Fn(=)1107 b Fl(S)15263 44896 y Fg(\303)16606 45507 y Fq(N)17353 45618 y Fd(s)16353 45906 y Fg(Y)16315 48696 y Fq(n)p Fk(=1)18310 47168 y Fl(d)18986 47367 y Fq(n)19612 44896 y Fg(!)21516 45507 y Fq(s)20885 45906 y Fg(Y)20987 48735 y Fq(l)11 b Fk(=1)22804 45693 y Fg(h\263)24224 47168 y Fl(I)399 b Fn(+)295 b Fl(O)27756 45693 y Fg(\263)28549 47168 y Fl(l)28965 46585 y Fi(\241)30353 46223 y Fd(\256)p 29830 46384 V 29830 46933 a Fe(1)p Fc(\241)p Fd(\256)31598 45693 y Fg(\264)q(\264)33406 47168 y Fn(exp)222 b(\()p Fh(\241)f Fn(\(1)296 b(+)e Fl(")40742 47367 y Fq(l)41089 47168 y Fn(\))221 b Fl(D)36 b Fn(\))43438 45693 y Fg(i)44286 47168 y Fl(S)45163 46619 y Fi(\241)p Fk(1)46421 47168 y Fl(:)3773 b Fn(\(4.8\))1636 51214 y(But)8794 51345 y Fg(\263)9587 52820 y Fl(I)399 b Fn(+)295 b Fl(O)13119 51345 y Fg(\263)13912 52820 y Fl(l)14328 52237 y Fi(\241)15716 51875 y Fd(\256)p 15193 52036 V 15193 52584 a Fe(1)p Fc(\241)p Fd(\256)16961 51345 y Fg(\264)q(\264)18769 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Fn(also)435 b(in)e(the)h(case)g Fl(\256)377 b Fn(=)369 b(1.)1636 68740 y(Finally)-108 b(,)447 b(for)c Fl(\270)385 b Fn(=)g(0)443 b(direct)g(computation)g(sho)-36 b(ws)443 b(that)g(0)386 b Fh(2)e Fl(\276)32867 68939 y Fq(p)33397 68740 y Fn(\()p Fl(J)123 b Fn(\))442 b(if)i(and)f(only)h(if)f Fl(a)385 b(>)g Fn(0.)608 b(The)443 b(pro)36 b(of)-315 70345 y(of)434 b(Theorem1.2)h(is)f(no)-36 b(w)434 b(complete.)26132 74188 y(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop -315 2274 a Fo(Remark)499 b(4.1)650 b Ff(Whether)551 b(the)h(b)-66 b(oundary)552 b(p)-66 b(oints)551 b Fl(\270)529 b Fn(=)h Fh(\247)29094 1641 y Fi(j)p Fq(a)p Fi(j)p 29094 1969 1023 54 v 29285 2733 a Fq(L)30801 2274 y Ff(do)552 b(b)-66 b(elong)551 b(to)h Fl(\276)39074 2473 y Fq(p)39603 2274 y Fn(\()p Fl(J)123 b Fn(\))551 b Ff(is)h(an)g(op)-66 b(en)551 b(question)-315 3880 y(\(we)465 b(c)-66 b(onje)g(ctur)g(e)463 b(they)h(do)h(not\).)-315 6261 y Fo(Remark)499 b(4.2)650 b Ff(In)454 b(the)h(next)e(se)-66 b(ction)453 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46980 y Fn(+)295 b Fl(c)20132 47179 y Fk(2)20658 46980 y Fn(\))221 b(\(2)p Fl(n)p Fn(\))23823 46431 y Fi(\241)p Fq(\256)25510 46980 y Fn(+)26817 45904 y Fg(\241)27426 46980 y Fl(c)27986 46431 y Fk(2)27986 47308 y(1)28806 46980 y Fn(+)295 b Fl(c)30673 46431 y Fk(2)30673 47308 y(2)31199 45904 y Fg(\242)32029 46980 y Fn(\(2)p Fl(n)p Fn(\))34467 46431 y Fi(\241)p Fk(2)p Fq(\256)36625 46980 y Fh(\241)g Fl(\256)8 b(n)39564 46431 y Fi(\241)p Fk(1)13550 49642 y Fh(\241)295 b Fn(2)p Fl(\256)8 b(c)16923 49841 y Fk(1)17671 49642 y Fn([)q(\(2)p Fl(n)p Fn(\))20471 49094 y Fq(\256)21131 49642 y Fn(2)p Fl(n)p Fn(])22919 48996 y Fi(\241)p Fk(1)24472 49642 y Fn(+)25911 48743 y(1)p 25911 49336 V 25911 50553 a(4)26916 48566 y Fg(\241)27525 49642 y Fn(2)p Fl(\256)29010 49094 y Fk(2)29832 49642 y Fh(\241)295 b Fl(\256)31995 48566 y Fg(\242)32826 49642 y Fl(n)33602 49094 y Fi(\241)p Fk(2)35155 49642 y Fn(+)g Fl(O)37714 48566 y Fg(\241)38322 49642 y Fl(n)39098 49094 y Fi(\241)p Fk(2)p Fi(\241)p Fq(\256)41693 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b(pro)-36 b(v)g(es)433 b(the)h(desired)f(estimate)g(of)i Fh(k)p Fl(J)123 b(f)142 b Fh(k)24923 59540 y Fk(2)25882 60022 y Fn(for)434 b Fl(f)511 b Fh(2)369 b Fl(M)31534 60221 y Fq(e)32026 60022 y Fn(.)1636 61627 y(In)404 b(the)f(case)h Fl(f)511 b Fh(2)368 b Fl(M)11829 61826 y Fk(0)12759 61627 y Fn(one)404 b(could)g(rep)36 b(eat)403 b(similar)i(estimates)f(but)e(w)-36 b(e)404 b(shall)h(use)e(the)g(follo)-36 b(wing)406 b(simple)-315 63232 y(observ)-72 b(ation.)1636 64838 y(Let)421 b Fl(U)4976 64356 y Fq(e)5890 64838 y Fn(\(resp.)g Fl(U)10520 64356 y Fq(o)11030 64838 y Fn(\))g(b)36 b(e)422 b(the)f(canonical)h (isometries)g(mapping)g Fl(l)33464 64356 y Fk(2)34412 64838 y Fn(on)-36 b(to)421 b Fl(M)38584 65037 y Fq(e)39498 64838 y Fn(\(resp.)573 b Fl(M)44516 65037 y Fq(o)45027 64838 y Fn(\))421 b(and)g(giv)-36 b(en)422 b(b)-36 b(y)-315 66443 y Fl(U)707 65961 y Fq(e)1199 66443 y Fl(e)1802 66642 y Fq(n)2797 66443 y Fn(=)369 b Fl(e)4781 66642 y Fk(2)p Fq(n)6311 66443 y Fn(\(resp.)577 b Fl(U)11097 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