Content-Type: multipart/mixed; boundary="-------------0510240405844" This is a multi-part message in MIME format. ---------------0510240405844 Content-Type: text/plain; name="05-366.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-366.keywords" spectral theory, random Schr\"odinger operators ---------------0510240405844 Content-Type: application/postscript; name="minimum.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="minimum.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: minimum.dvi %%CreationDate: Mon Oct 24 11:36:44 2005 %%Pages: 19 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMBX12 CMR8 CMBX10 CMR10 CMMI10 CMMI8 %%+ CMSY10 CMSS10 CMMI12 CMR7 MSBM10 CMEX10 CMSY8 MSBM7 CMMI6 CMTI8 %%+ CMTI12 CMSY6 CMR6 MSAM10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf minimum %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2005.10.24:1135 %%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 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. 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 175 /vextendsingle put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 80 /summationtext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 101 /tildewide put dup 112 /radicalbig put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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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 (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 175 /fi put dup 45 /hyphen put 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 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T 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 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 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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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 43 /plus put 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: 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 dup 164 /asteriskmath put dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 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 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M 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 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 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 196 /dieresis put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI8 %!PS-AdobeFont-1.1: CMTI8 1.0 %%CreationDate: 1991 Aug 18 21:07:42 % 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 (CMTI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI8 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 101 /e put dup 112 /p put dup 114 /r put readonly def /FontBBox{-35 -250 1190 750}readonly def /UniqueID 5000826 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 176 /gamma put dup 184 /lambda put dup 33 /omega put dup 59 /comma put dup 100 /d put dup 107 /k put dup 109 /m put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % 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 (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 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 67 /C put dup 78 /N put dup 82 /R put dup 84 /T put dup 90 /Z put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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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 162 /periodcentered put dup 164 /asteriskmath put dup 169 /circleplus put dup 173 /circlemultiply put dup 177 /openbullet put dup 183 /lessequal put dup 184 /greaterequal put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 69 /E put dup 80 /P put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 67 /C put dup 82 /R put dup 84 /T put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 1D432B0D064B56C598F4338C319309181D78E1629A31ECA5DD8536379B03C383 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%%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % 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 (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 162 /Delta put dup 175 /fi put dup 182 /acute put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 52 /four put dup 53 /five put dup 61 /equal put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U 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 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 196 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 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 49 /one put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % 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 (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 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 162 /periodcentered put dup 163 /multiply put dup 173 /circlemultiply put dup 178 /bullet put dup 183 /lessequal put dup 184 /greaterequal put dup 189 /propersubset put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 59 /emptyset put dup 60 /Rfractur put dup 69 /E put dup 72 /H put dup 76 /L put dup 80 /P put dup 83 /S put dup 84 /T put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % 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 (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 166 /Pi put dup 167 /Sigma put dup 174 /ff put dup 175 /fi put dup 191 /oslash put dup 195 /suppress 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 59 /semicolon 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 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex 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 196 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 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CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % 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 (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 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 175 /fi put dup 44 /comma 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 58 /colon put dup 65 /A put dup 67 /C put dup 70 /F put dup 75 /K put dup 77 /M put dup 80 /P put dup 81 /Q put dup 83 /S put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put dup 196 /dieresis put 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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % 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 (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 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 176 /gamma put dup 177 /delta put dup 181 /theta put dup 184 /lambda put dup 33 /omega put dup 39 /phi1 put dup 59 /comma put dup 67 /C put dup 72 /H put dup 76 /L put dup 78 /N put dup 97 /a put dup 99 /c put dup 100 /d 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 115 /s put dup 120 /x put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 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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 184 /lambda put dup 59 /comma put dup 62 /greater put dup 72 /H put dup 86 /V put dup 87 /W put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E 6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF 8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE 03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 AFC0E2F840512D321166547B306C592B8A01E1FA2564B9A26DAC14256414E4C8 42616728D918C74D13C349F4186EC7B9708B86467425A6FDB3A396562F7EE4D8 40B43621744CF8A23A6E532649B66C2A0002DD04F8F39618E4F572819DD34837 B5A08E643FDCA1505AF6A1FA3DDFD1FA758013CAED8ACDDBBB334D664DFF5B53 95601766730045C2D9F29DC2BFEBDE5E7720CC7D8252348B3466132A2AE7067E FCA5031C817BB7DCE127F3C50AD7474494609C272AF15DC1C26DE4ED937F0446 59AC6220C63D6FC17E4C161E6519FBAA06265B7EACDBA2760C63D0AFF582EB67 CB2BA9C1FC36F7A1D19F2A24ACB66047443EE6EF089BF3362EB573507694375C 5EF90ECE944589B09A3F843D9A1CD5C9D0A49B3185FD0246410D44F39688A4FE 095E89E08CB353C28B09155F8763F8A48156681FC796CAC0F76362D9B1329E35 A82897A9814E826C207211C1FD1B4FC626286CECDC7F3BDDC4F39005EA698CBA 0A0392B527A93602032E60BC2003983026FF67B7F824F512828044F957255643 B2E912EC5C86D02C8C1CEAD768A7925CBFBE13967CB7045A0B5A7E8C60D51A0F D6F7EFFA8664BA4AAF4891E77342F659B9A887CA14B9E713A56AD62321CCA0BD DA540D69B6B348F92C69F86072EB10D1545E8C37147996B62139CFD3271E8CD0 84E3C393E3B25178E11F8A4CD623B2B396D9E01BAA1C2EA5CE6EE68BFE775CA0 BEEA97EEB6E56CC1985B62643B5226DC10697568EA68DB2B6AE17895D6111D89 15B798697114129EE7BA028C197FD7FC716D749E71723FA9A01B91A3D02AF3AA 16C2FF246849CBFAEE37B15A820112332E78BE44F84AB4AC8901CD2D2577F2A6 A429EDDC0D96314D197EC22239894D05E42F389BB78F80733EFDA39A56E58FE9 8958A7C7ECC959A152AD108C81AAF2EDBD8129D4484AADF09BF0D1303EC2DCAD DD2146133A64FF0F7397901956998F33B16B6688BE22D58D45D2F141DFCF3883 21A14DB0AE18152CA52A10A41CCD8B665779C54C45A913464D2F7C70647BB364 B2C22CFA0ADAB5421A78F1672D21A5AAC5312A87E3999D9F1F6D145179DDC048 40735342EA752389082AD592B9BA622CCD8F2B21400EEA3FDA7A8F771444D177 C236E03B016ABEC7FCBA45A356B23A9F3B4716DF8A53908E29B6C86C7E94C4EF 9B79488952FAA19F062D29D19AAA4DF5C8D7098DBC3FFF19672800BB7A38D16C 2E62879E7EE92A4CED422DE0BB011148E42A390CA4BEBC0C087AC82EBA6D3210 13A95CE31B5CF313C71F1025DCD4252B3CB94F4003C39A300E84A736ABDF5BD3 FF43B617E6BAC529F32BC95997F3407567D540DBCA130024585E4CACD6427DB6 392528A5A035B61FB340A21DA9B9C78E22F67FD21BE73D1320FF68F99FD132F7 F06DB528A209041A75F80FBAC68E4F10EA9258F82830CD68D2840EBE6FF4D1FC 8A0FE7A8C7AF9BB470A0AB61EC06B0339EE2A63389906574231A2D8933EA6D11 6C3B3B72E2E9364167CD95E5AB8A30C734F9FD24F1F5526619436E26939A783B C8D5588339580790452FE6DAE144EE5C8CFDE49D5D8CF1EEDD5FDF001F24F777 2D16F8931D8511745211DC1C323ED2B698EBE08EAFA072B1E5C561FB4954A0DD 92F405251B086A9CE9A5C3CDF341DF017801390D0F0EE47F8BF263B1507BD06C DD74361F5668358992A19CF53C072CBA14E9F861BC0B888BBCE1441F5F61F536 21E0FBFD3066F6F20B3F7F6E7C4EF813490F57BC80221EBEDBBB14F50054F59A 2CE3E98441EA5FF122DD3403B5A8731491333EF7B90BC5F93A63DB200C932941 108D5D85600E78B0AC4CFA6D816A22F9B88CDE3A0B3BB32BB703B3BAC4AEB2B7 80E305916D06F3FB423778C46F26AAD21042FC8F4D94E59973D2275BEFF2C03D 6DE59649BD95E41C0B748C3700C7BF728B3DC2C436E89529B3FBFD54A36D3A49 74514E98E8623648958005081E355A5795651FD6C72F4C37C0BCBAE99703BF1D 8F23F852CC 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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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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 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 59 /semicolon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 99 /c put dup 101 /e put dup 108 /l put dup 111 /o put dup 112 /p put dup 114 /r put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % 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. 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Fl(e)-798 b Fq(!)32622 59399 y Fv(\260)33295 59200 y Fr(^)-731 b Fq(u)q Fr(\()p Fq(\260)72 b Fr(\))p 35714 58045 2436 54 v 49 w(^)-699 b Fq(v)47 b Fr(\()p Fq(\260)72 b Fr(\))38148 57673 y Fl(\257)38148 58470 y(\257)38148 59267 y(\257)4686 63008 y Fp(\267)369 b Fq(C)95 b(\257)8302 61746 y Fl(X)8144 64674 y Fv(\260)52 b Fk(2)p Fj(Z)9898 64421 y Fi(d)10661 63008 y Fl(e)-797 b Fq(!)11412 63207 y Fv(\260)12004 63008 y Fr(\()p Fp(j)81 b Fr(^)-731 b Fq(u)p Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)15747 62460 y Fz(2)16272 63008 y Fr(+)p Fp(j)49 b Fr(^)-699 b Fq(v)47 b Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)20457 62460 y Fz(2)20983 63008 y Fr(\)+)p Fq(C)95 b Fr(\(1+1)p Fq(=\257)74 b Fr(\)\()p Fp(h)p Fq(\263)29900 63207 y Fv(k)24 b(;\270)31278 63008 y Fq(u;)221 b(u)p Fp(i)33857 63231 y Fv(L)34497 62979 y Fe(2)34959 63231 y Fz(\()p Fj(T)35915 62979 y Ff(\244)36395 63231 y Fz(\))36816 63008 y Fr(+)p Fp(h)p Fq(\263)38913 63207 y Fv(k)39427 62955 y Ff(0)39724 63207 y Fv(;\270)40590 63008 y Fq(v)48 b(;)221 b(v)48 b Fp(i)43043 63231 y Fv(L)43683 62979 y Fe(2)44143 63231 y Fz(\()p Fj(T)45099 62979 y Ff(\244)45579 63231 y Fz(\))46000 63008 y Fr(\))p Fq(:)44650 66213 y Fr(\(3.10\))25578 70015 y(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 8434 7505 a Fp(k)p Fq(V)9903 7704 y Fc(e)-570 b Fv(!)10529 7505 y Fp(T)11252 7704 y Fv(')11865 7860 y Fi(k)12429 7505 y Fr(\()p Fq(u)p Fr(\))p Fp(k)14845 6957 y Fz(2)14845 7883 y Fv(L)15485 7630 y Fe(2)15946 7883 y Fz(\()p Fj(R)16952 7630 y Fi(d)17433 7883 y Fz(\))18224 7505 y Fp(\267)369 b Fq(C)20652 6031 y Fl(\263)21825 6243 y(X)21666 9171 y Fv(\260)52 b Fk(2)p Fj(Z)23420 8918 y Fi(d)24184 7505 y Fl(e)-797 b Fq(!)24935 7704 y Fv(\260)25527 7505 y Fp(j)81 b Fr(^)-731 b Fq(u)p Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)28764 6957 y Fz(2)29584 7505 y Fr(+)295 b Fp(h)p Fq(\263)31976 7704 y Fv(k)24 b(;\270)33355 7505 y Fq(u;)221 b(u)p Fp(i)35934 7728 y Fv(L)36574 7476 y Fe(2)37036 7728 y Fz(\()p Fj(T)37992 7476 y Ff(\244)38472 7728 y Fz(\))38893 6031 y Fl(\264)39687 7505 y Fq(:)4117 b Fr(\(3.11\))4317 12641 y Fd(3.1)1793 b(If)597 b Fb(A)p FB(\(0\))i Fd(is)f(p)50 b(ositiv)-50 b(e-de\257nite)4317 15104 y Fr(W)-108 b(e)434 b(set)11336 16709 y Fq(H)12517 16160 y Fz(0)12414 17037 y Fv(\270;!)14265 16709 y Fr(=)368 b(\246)16620 16908 y Fv(\270;)p Fz(0)17956 16709 y Fq(H)19034 16908 y Fv(\270;)47 b Fc(e)-570 b Fv(!)20516 16709 y Fr(\246)21491 16908 y Fv(\270;)p Fz(0)23196 16709 y Fr(=)369 b(\246)25552 16908 y Fv(\270;)p Fz(0)26888 16709 y Fq(H)27966 16928 y Fv(\270;!)29393 16675 y Ff(\241)30143 16709 y Fr(\246)31118 16908 y Fv(\270;)p Fz(0)32749 16709 y Fr(+)295 b(\246)35031 16908 y Fv(\270;)p Fz(0)36367 16709 y Fq(V)37172 16908 y Fc(e)-570 b Fv(!)37798 16709 y Fr(\246)38773 16908 y Fv(\270;)p Fz(0)40109 16709 y Fq(:)4317 19753 y FA(Theorem)499 b(3.3)651 b Fg(Assume)476 b(that)g(the)g(matrix)f Fq(A)p Fr(\(0\))h Fg(is)g(p)-66 b(ositive-de\257nite.)472 b(Then)k(ther)-66 b(e)4317 21358 y(exists)465 b Fq(\270)8630 21557 y Fz(0)9524 21358 y Fq(>)369 b Fr(0)465 b Fg(such)h(that)e(for)h (any)f Fq(\270)369 b Fp(2)g Fr([0)p Fq(;)221 b(\270)26933 21557 y Fz(0)27460 21358 y Fr(])465 b Fg(we)g(have:)12080 24657 y Fr(\246)13055 24856 y Fv(\270;)p Fz(0)14391 23182 y Fl(\263)15184 24657 y Fq(H)16262 24856 y Fv(\270;!)18039 24657 y Fp(\241)296 b Fq(E)20331 24876 y Fv(\270;!)21758 24623 y Ff(\241)22508 23182 y Fl(\264)23301 24657 y Fr(\246)24276 24856 y Fv(\270;)p Fz(0)27007 24657 y Fg(is)465 b(a)930 b(p)-66 b(ositive)463 b(op)-66 b(er)g(ator.)4317 27992 y Fr(The)434 b(pro)36 b(of)434 b(of)g(Theorem)g(3.3)g(is)g(the)f(ob)72 b(ject)434 b(of)h(the)e(follo)-36 b(wing)436 b(section.)4317 31456 y FA(3.1.1)1495 b(The)499 b(pro)42 b(of)498 b(of)g(Theorem)h(3.3) 4317 33919 y Fr(Using)434 b(\(3.8\),)g(w)-36 b(e)434 b(get)g(that)f Fq(H)19523 33437 y Fz(0)19420 34265 y Fv(\270;!)21336 33919 y Fr(is)h(unitarly)f(equiv)-72 b(alen)-36 b(t)435 b(to)e(the)g(op)36 b(erator)19858 36995 y Fq(h)20607 36447 y Fz(0)20607 37323 y Fv(\270;!)22458 36995 y Fr(=)368 b Fp(T)24899 36447 y Fk(\244)24561 37323 y Fv(')25174 37479 y Fi(\270;)p Fe(1)26433 36995 y Fq(H)27614 36447 y Fz(0)27511 37323 y Fv(\270;!)28993 36995 y Fp(T)29716 37194 y Fv(')30329 37350 y Fi(\270;)p Fe(1)31587 36995 y Fq(;)4317 40101 y Fr(acting)434 b(on)g Fq(L)10911 39618 y Fz(2)11436 40101 y Fr(\()p Fm(T)12828 39618 y Fk(\244)13354 40101 y Fr(\))f(and)g(written)g(as)19968 43034 y Fq(h)20717 42486 y Fz(0)20717 43362 y Fv(\270;!)22568 43034 y Fr(=)369 b Fq(h)24698 42486 y Fz(0)24698 43375 y Fv(\270;!)26125 43122 y Ff(\241)27170 43034 y Fr(+)295 b Fq(\270V)30283 42486 y Fz(0)29994 43362 y Fv(\270;)47 b Fc(e)-570 b Fv(!)31476 43034 y Fq(:)4317 45967 y Fr(With)432 b Fq(h)8424 45485 y Fz(0)8424 46374 y Fv(\270;!)9851 46122 y Ff(\241)11033 45967 y Fr(is)g(the)f(m)-36 b(ultiplication)432 b(op)36 b(erator)432 b(b)-36 b(y)432 b Fq(E)30926 46166 y Fz(1)31452 45967 y Fr(\()p Fq(\270;)221 b(\265)36 b Fr(\))432 b(and)f Fq(V)38453 45485 y Fz(0)38164 46337 y Fv(\270;)47 b Fc(e)-570 b Fv(!)40078 45967 y Fr(is)432 b(an)g(in)-36 b(tegral)4317 47573 y(op)36 b(erator)434 b(with)g(the)f(k)-36 b(ernel)15660 50506 y Fq(V)16418 50705 y Fv(\270;)47 b Fc(e)-570 b Fv(!)17901 50506 y Fr(\()p Fq(\265)36 b(;)221 b(\265)20273 49958 y Fk(0)20585 50506 y Fr(\))368 b(=)h Fp(h)p Fq(V)24162 50705 y Fc(e)-570 b Fv(!)24787 50506 y Fq(')25639 50705 y Fv(\270;)p Fz(1)26975 50506 y Fr(\()p Fp(\242)p Fq(;)221 b(\265)36 b Fr(\))p Fq(;)221 b(')31014 50705 y Fv(\270;)p Fz(1)32351 50506 y Fr(\()p Fp(\242)p Fq(;)g(\265)34450 49958 y Fk(0)34762 50506 y Fr(\))p Fp(i)p Fq(:)4317 53439 y Fr(Let)439 b Fq(V)7411 53638 y Fv(k)8419 53439 y Fr(b)36 b(e)438 b(a)i(neigh)-36 b(b)36 b(orho)g(o)g(d)438 b(of)i Fq(\265)21547 53638 y Fv(k)22116 53439 y Fr(,)f(suc)-36 b(h)438 b(that)h(if)g Fq(\265)30482 53638 y Fv(k)30996 53387 y Ff(0)31728 53439 y Fp(2)377 b Fq(Z)535 b Fr(and)438 b Fq(k)423 b Fp(6)p Fr(=)378 b Fq(k)40160 52957 y Fk(0)40910 53439 y Fr(then)437 b Fq(\265)569 b(=)-804 b Fp(2)p 46161 52372 1328 54 v 377 w Fq(V)46919 53638 y Fv(k)4317 55045 y Fr(and)625 b Fq(V)7796 55244 y Fv(k)8791 55045 y Fp(\\)425 b Fq(V)10860 55244 y Fv(k)11374 54992 y Ff(0)12423 55045 y Fr(=)695 b Fp(;)p Fr(.)627 b(As)e Fm(T)18781 54562 y Fk(\244)19932 55045 y Fr(is)h(compact,)g(one)f(can)g(co)-36 b(v)g(er)626 b(it)g(b)-36 b(y)625 b(\()p Fq(V)40647 55244 y Fv(k)41216 55045 y Fr(\))41722 55244 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)45682 55045 y Fr(\(i.e)4317 56650 y Fp([)5203 56849 y Fz(1)p Fk(\267)p Fv(k)g Fk(\267)p Fv(m)8538 56650 y Fq(V)9296 56849 y Fv(k)10234 56650 y Fr(=)369 b Fm(T)12501 56101 y Fk(\244)13026 56650 y Fr(\).)434 b(F)-108 b(or)433 b(1)369 b Fp(\267)g Fq(k)414 b Fp(\267)370 b Fq(m)433 b Fr(let)h Fq(\302)25836 56849 y Fv(k)26838 56650 y Fr(b)36 b(e)433 b(the)g(c)-36 b(haracteristic)434 b(function)f(of)i Fq(V)46174 56849 y Fv(k)46743 56650 y Fr(.)4317 58255 y(F)-108 b(or)582 b(simplicit)-36 b(y)583 b(for)g Fq(u)623 b Fp(2)f Fq(L)18769 57773 y Fz(2)19294 58255 y Fr(\()p Fm(T)20686 57773 y Fk(\244)21212 58255 y Fr(\),)582 b(w)-36 b(e)583 b(will)h(denote)d Fq(\302)32485 58454 y Fv(k)33054 58255 y Fq(u)i Fr(as)g Fq(u)36863 58454 y Fv(k)38014 58255 y Fr(in)f(the)g(follo)-36 b(wing.)4317 59860 y(W)-108 b(e)479 b(consider)g Fq(u)h Fr(as)f(a)h(system)f(of)h Fq(m)f Fr(columns)g(denoted)f(b)-36 b(y)479 b(\()p Fq(u)36376 60059 y Fv(k)36945 59860 y Fr(\))37451 60059 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)40786 59860 y Fr(.)480 b(W)-108 b(e)479 b(endo)-36 b(w)4317 61465 y Fq(L)5202 60983 y Fz(2)5728 61465 y Fr(\()p Fm(T)7120 60983 y Fk(\244)7645 61465 y Fr(\))19 b Fp(\255)g Fm(C)10181 60983 y Fv(m)11368 61465 y Fr(with)298 b(the)g(scalar)h(pro)36 b(duct)297 b(generating)i(the)f(follo)-36 b(wing)300 b(Euclidean)f(norm:)17389 64631 y Fp(k)p Fq(u)p Fp(k)19457 64082 y Fz(2)19457 64975 y Fv(L)20097 64723 y Fe(2)20559 64975 y Fz(\()p Fj(T)21515 64723 y Ff(\244)21995 64975 y Fz(\))p Fk(\255)p Fj(C)23733 64723 y Fi(m)24939 64631 y Fr(=)26319 63369 y Fl(X)26421 66198 y Fv(k)24 b Fz(=1)28459 64631 y Fp(k)p Fq(u)29863 64830 y Fv(k)30433 64631 y Fp(k)31097 64082 y Fz(2)31097 64975 y Fv(L)31737 64723 y Fe(2)32198 64975 y Fz(\()p Fj(T)33154 64723 y Ff(\244)33634 64975 y Fz(\))34055 64631 y Fq(:)25253 70015 y Fr(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 4317 7306 a FA(3.1.2)1495 b(The)499 b(lo)-42 b(w)g(er)500 b(b)42 b(ound)499 b(of)e Fq(h)22940 6824 y Fz(0)22940 7713 y Fv(\270;!)24367 7461 y Ff(\241)4317 9906 y FA(Prop)42 b(osition)500 b(3.4)651 b Fg(Ther)-66 b(e)427 b(exists)g Fq(C)464 b(>)369 b Fr(0)428 b Fg(such)h(that)f(for)g (any)f Fq(u)370 b Fp(2)e Fq(L)39300 9424 y Fz(2)39826 9906 y Fr(\()p Fm(T)41218 9424 y Fk(\244)41743 9906 y Fr(\))p Fg(,)427 b(we)i(have)6116 13024 y Fp(h)p Fq(h)7382 12476 y Fz(0)7382 13365 y Fv(\270;!)8809 13113 y Ff(\241)9559 13024 y Fq(u;)221 b(u)p Fp(i)369 b(\270)14590 11762 y Fl(X)13910 14591 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)17411 13024 y Fq(E)18374 13223 y Fz(1)18900 13024 y Fr(\()p Fq(\270;)221 b(\265)21353 13223 y Fv(k)21922 13024 y Fr(\()p Fq(\270)p Fr(\)\))p Fp(k)p Fq(u)25603 13223 y Fv(k)26171 13024 y Fp(k)26835 12476 y Fz(2)26835 13369 y Fv(L)27475 13116 y Fe(2)27937 13369 y Fz(\()p Fj(T)28893 13116 y Ff(\244)29373 13369 y Fz(\))30089 13024 y Fr(+)31716 12126 y(1)p 31529 12719 1026 54 v 31529 13936 a Fq(C)33589 11762 y Fl(X)32909 14591 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)36189 13024 y Fp(h)p Fq(\263)37274 13223 y Fv(k)g(;\270)38653 13024 y Fq(u)39393 13223 y Fv(k)39962 13024 y Fq(;)221 b(u)41284 13223 y Fv(k)41853 13024 y Fp(i)42370 13247 y Fv(L)43010 12995 y Fe(2)43471 13247 y Fz(\()p Fj(T)44427 12995 y Ff(\244)44907 13247 y Fz(\))45328 13024 y Fq(:)44165 15980 y Fr(\(3.12\))4317 18559 y FA(Pro)42 b(of:)434 b Fr(F)-108 b(or)433 b Fq(u)369 b Fp(2)f Fq(L)14368 18076 y Fz(2)14894 18559 y Fr(\()p Fm(T)16286 18076 y Fk(\244)16811 18559 y Fr(\),)434 b(one)g(computes) 6147 21730 y Fp(h)p Fq(h)7413 21181 y Fz(0)7413 22070 y Fv(\270;!)8840 21818 y Ff(\241)9590 21730 y Fq(u;)221 b(u)p Fp(i)370 b Fr(=)13919 19922 y Fl(Z)14657 22929 y Fj(T)15247 22677 y Ff(\244)16004 21730 y Fq(E)16967 21929 y Fz(1)17493 21730 y Fr(\()p Fq(\270;)221 b(\265)36 b Fr(\))p Fp(j)p Fq(u)p Fr(\()p Fq(\265)g Fr(\))p Fp(j)23620 21181 y Fz(2)24146 21730 y Fq(d\265)405 b Fr(=)27894 20468 y Fl(X)27214 23297 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)30715 19922 y Fl(Z)31453 22929 y Fj(T)32043 22677 y Ff(\244)32800 21730 y Fq(E)33763 21929 y Fz(1)34288 21730 y Fr(\()p Fq(\270;)221 b(\265)36 b Fr(\))p Fq(\302)38098 21929 y Fv(k)38667 21730 y Fr(\()p Fq(\265)g Fr(\))p Fp(j)p Fq(u)p Fr(\()p Fq(\265)g Fr(\))p Fp(j)43453 21181 y Fz(2)43979 21730 y Fq(d\265)g(;)4317 25533 y Fr(As)434 b(for)g(an)-36 b(y)434 b Fq(\265)470 b Fr(in)433 b Fq(V)14034 25732 y Fv(k)15037 25533 y Fr(the)g(supp)36 b(ort)432 b(of)i Fq(\302)24385 25732 y Fv(k)24954 25533 y Fr(,)g(there)f(exists)h Fq(C)464 b(>)369 b Fr(0)434 b(suc)-36 b(h)432 b(that)h(w)-36 b(e)434 b(ha)-36 b(v)g(e)15954 28577 y Fq(E)16917 28776 y Fz(1)17442 28577 y Fr(\()p Fq(\270;)221 b(\265)19895 28776 y Fv(k)20465 28577 y Fr(\()p Fq(\270)p Fr(\)\))294 b(+)24663 27678 y(1)p 24476 28271 V 24476 29488 a Fq(C)25634 28577 y(\263)26202 28776 y Fv(k)24 b(;\270)27582 28577 y Fr(\()p Fq(\265)36 b Fr(\))369 b Fp(\267)g Fq(E)31970 28776 y Fz(1)32495 28577 y Fr(\()p Fq(\270;)221 b(\265)36 b Fr(\))p Fq(;)4317 31442 y Fr(w)-36 b(e)434 b(get)g(the)f(result.) 32267 b Fa(\244)4317 34845 y FA(3.1.3)1495 b(The)499 b(lo)-42 b(w)g(er)500 b(b)42 b(ound)499 b(of)e Fq(V)23239 34363 y Fz(0)22949 35215 y Fv(\270;)47 b Fc(e)-570 b Fv(!)4317 37308 y FA(Prop)42 b(osition)500 b(3.5)651 b Fg(Ther)-66 b(e)402 b(exists)h Fq(C)23048 37507 y Fz(1)23573 37308 y Fq(;)221 b(C)25086 37507 y Fz(2)25981 37308 y Fq(>)369 b Fr(0)403 b Fg(and)h Fq(\270)31637 37507 y Fz(0)32565 37308 y Fg(such)g(that)f(for)g(al)66 b(l)404 b Fq(\270)369 b Fp(2)f Fr([0)p Fq(;)221 b(\270)46600 37507 y Fz(0)47127 37308 y Fr(])4317 38913 y Fg(and)465 b Fq(u)369 b Fp(2)g Fq(L)10090 38431 y Fz(2)10616 38913 y Fr(\()p Fm(T)12008 38431 y Fk(\244)12533 38913 y Fr(\))465 b Fg(we)g(have)5435 41671 y Fp(h)p Fq(V)6998 41123 y Fz(0)6710 42000 y Fv(\270;)47 b Fc(e)-570 b Fv(!)8192 41671 y Fq(u;)221 b(u)p Fp(i)370 b(\270)f Fq(C)13474 41870 y Fz(1)16150 40410 y Fl(X)14221 43337 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m;\260)52 b Fk(2)p Fj(Z)19516 43085 y Fi(d)20280 41671 y Fl(e)-798 b Fq(!)21030 41870 y Fv(\260)21622 41671 y Fp(j)p Fr(\()329 b(^)-979 b Fq(u)23237 41870 y Fv(k)23806 41671 y Fr(\)\()p Fq(\260)72 b Fr(\))p Fp(j)26440 41123 y Fz(2)27260 41671 y Fp(\241)296 b Fq(C)29520 41870 y Fz(2)30947 40410 y Fl(X)30266 43238 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)33546 41671 y Fp(h)p Fq(\263)34631 41870 y Fv(k)g(;\270)36010 41671 y Fq(u)36750 41870 y Fv(k)37319 41671 y Fq(;)221 b(u)38641 41870 y Fv(k)39211 41671 y Fp(i)39728 41894 y Fv(L)40368 41642 y Fe(2)40829 41894 y Fz(\()p Fj(T)41785 41642 y Ff(\244)42265 41894 y Fz(\))42686 41671 y Fq(:)1118 b Fr(\(3.13\))4317 45648 y FA(The)499 b(pro)42 b(of)498 b(of)g(Theorem)h(3.3)4317 47253 y Fr(Let)450 b(us)g(notice)h(that,)g(b)-36 b(y)450 b(com)-36 b(bining)451 b(the)f(results)g(of)h(Prop)36 b(osition)451 b(3.4)h(and)e(3.5,)i(one)4317 48858 y(gets)639 b(that)e(there)h(exists)h Fq(\270)18309 49057 y Fz(0)19551 48858 y Fq(>)717 b Fr(0)639 b(suc)-36 b(h)637 b(that)h(for)g(an)-36 b(y)639 b Fq(\270)717 b Fp(2)g Fr([0)p Fq(;)221 b(\270)39014 49057 y Fz(0)39540 48858 y Fr(])639 b(and)f(for)g(an)-36 b(y)4317 50463 y Fq(u)369 b Fp(2)g Fq(L)7566 49981 y Fz(2)8092 50463 y Fr(\()p Fm(T)9484 49981 y Fk(\244)10442 50463 y Fr(w)-36 b(e)434 b(ha)-36 b(v)g(e,)4709 53581 y Fp(h)p Fq(h)5975 53033 y Fz(0)5975 53910 y Fv(\270;!)7456 53581 y Fq(u;)221 b(u)p Fp(i)1108 b(\270)13964 52319 y Fl(X)13283 55148 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)16784 53581 y Fq(E)17747 53780 y Fz(1)18273 53581 y Fr(\()p Fq(\270;)221 b(\265)20726 53780 y Fv(k)21295 53581 y Fr(\()p Fq(\270)p Fr(\)\))p Fp(k)p Fq(u)24976 53780 y Fv(k)25545 53581 y Fp(k)26209 53033 y Fz(2)26209 53925 y Fv(L)26849 53673 y Fe(2)27310 53925 y Fz(\()p Fj(T)28266 53673 y Ff(\244)28746 53925 y Fz(\))29462 53581 y Fr(+)31090 52683 y(1)p 30902 53276 V 30902 54492 a Fq(C)32061 52107 y Fl(\263)33756 52319 y(X)33076 55148 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)36356 53581 y Fp(h)p Fq(\263)37441 53780 y Fv(k)g(;\270)38819 53581 y Fq(u)39559 53780 y Fv(k)40128 53581 y Fq(;)221 b(u)41450 53780 y Fv(k)42020 53581 y Fp(i)42537 53804 y Fv(L)43177 53552 y Fe(2)43638 53804 y Fz(\()p Fj(T)44594 53552 y Ff(\244)45074 53804 y Fz(\))45790 53581 y Fr(+)13283 57401 y Fq(\270)14944 56139 y Fl(X)14263 58968 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)17924 56139 y Fl(X)17765 59066 y Fv(\260)52 b Fk(2)p Fj(Z)19519 58814 y Fi(d)20282 57401 y Fl(e)-797 b Fq(!)21033 57600 y Fv(\260)21625 57401 y Fp(j)329 b Fr(^)-979 b Fq(u)22734 57600 y Fv(k)23303 57401 y Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)25431 56852 y Fz(2)25956 55926 y Fl(\264)11143 61569 y Fp(\270)1107 b Fq(E)14246 61788 y Fv(\270;!)15673 61535 y Ff(\241)16423 61569 y Fp(k)p Fq(u)p Fp(k)18491 61020 y Fz(2)18491 61913 y Fv(L)19131 61661 y Fe(2)19593 61913 y Fz(\()p Fj(T)20549 61661 y Ff(\244)21029 61913 y Fz(\))21745 61569 y Fr(+)23373 60670 y(1)p 23185 61263 V 23185 62480 a Fq(C)24344 60094 y Fl(\263)26039 60307 y(X)25359 63136 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)28639 61569 y Fp(h)p Fq(\263)29724 61768 y Fv(k)g(;\270)31102 61569 y Fq(u)31842 61768 y Fv(k)32411 61569 y Fq(;)221 b(u)33733 61768 y Fv(k)34303 61569 y Fp(i)34820 61791 y Fv(L)35460 61539 y Fe(2)35921 61791 y Fz(\()p Fj(T)36877 61539 y Ff(\244)37357 61791 y Fz(\))38073 61569 y Fr(+)13283 65388 y Fq(\270)14944 64126 y Fl(X)14263 66955 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)17924 64126 y Fl(X)17765 67053 y Fv(\260)52 b Fk(2)p Fj(Z)19519 66801 y Fi(d)20282 65388 y Fl(e)-797 b Fq(!)21033 65587 y Fv(\260)21625 65388 y Fp(j)329 b Fr(^)-979 b Fq(u)22734 65587 y Fv(k)23303 65388 y Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)25431 64840 y Fz(2)25956 63914 y Fl(\264)26750 65388 y Fq(:)25253 70015 y Fr(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 4317 7306 a Fr(This)434 b(giv)-36 b(es)435 b(that,)5424 10156 y Fp(h)p Fr(\()p Fq(h)7196 9607 y Fz(0)7196 10484 y Fv(\270;)47 b Fc(e)-570 b Fv(!)8973 10156 y Fp(\241)295 b Fq(E)11264 10375 y Fv(\270;!)12691 10123 y Ff(\241)13441 10156 y Fr(\))p Fq(u;)221 b(u)p Fp(i)370 b(\270)13223 11955 y Fr(1)p 13035 12548 1026 54 v 13035 13765 a Fq(C)14194 11379 y Fl(\263)15889 11592 y(X)15208 14421 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)18488 12854 y Fp(h)p Fq(\263)19573 13053 y Fv(k)g(;\270)20952 12854 y Fq(u)21692 13053 y Fv(k)22261 12854 y Fq(;)221 b(u)23583 13053 y Fv(k)24153 12854 y Fp(i)24670 13077 y Fv(L)25310 12824 y Fe(2)25771 13077 y Fz(\()p Fj(T)26727 12824 y Ff(\244)27207 13077 y Fz(\))27923 12854 y Fr(+)295 b Fq(\270)30891 11592 y Fl(X)30210 14421 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)33870 11592 y Fl(X)33711 14519 y Fv(\260)52 b Fk(2)p Fj(Z)35465 14267 y Fi(d)36229 12854 y Fl(e)-798 b Fq(!)36979 13053 y Fv(\260)37572 12854 y Fp(j)329 b Fr(^)-979 b Fq(u)38681 13053 y Fv(k)39250 12854 y Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)41378 12305 y Fz(2)41903 11379 y Fl(\264)42696 12854 y Fq(:)1108 b Fr(\(3.14\))4317 16770 y(This)434 b(ends)f(the)g(pro)36 b(of)434 b(of)g(Theorem)g(3.3.)21567 b Fa(\244)4317 20731 y FA(Remark)499 b(3.6)650 b Fg(We)370 b(notic)-66 b(e)368 b(that)i(even)f(if)g(we)h(know)h(that)e(the)h(b)-66 b(ottom)369 b(of)h(the)g(sp)-66 b(e)g(ctrum)4317 22336 y(of)419 b Fq(H)6877 22535 y Fv(!)7969 22336 y Fg(c)-66 b(oincides)418 b(with)h(the)h(b)-66 b(ottom)418 b(of)i(the)f(sp)-66 b(e)g(ctrum)419 b(of)g Fq(H)34173 22555 y Fv(\270;!)35600 22303 y Ff(\241)36770 22336 y Fg(we)g(c)-66 b(annot)419 b(c)-66 b(onsider)4317 24366 y Fr(\246)5292 24565 y Fv(\270;)p Fz(0)6628 22891 y Fl(\263)7422 24366 y Fq(H)8500 24565 y Fv(\270;!)10277 24366 y Fp(\241)295 b Fq(H)12683 24585 y Fv(\270;!)14110 24332 y Ff(\241)14860 22891 y Fl(\264)15654 24366 y Fr(\246)16629 24565 y Fv(\270;)p Fz(0)18430 24366 y Fg(as)465 b(a)g(p)-66 b(ositive)464 b(op)-66 b(er)g(ator.)4317 27013 y FA(The)499 b(pro)42 b(of)498 b(of)g(prop)42 b(osition)500 b(3.5:)4317 28618 y Fr(Let)433 b(us)g(start)h(b)-36 b(y)433 b(expanding)h Fp(h)p Fq(V)21052 28136 y Fz(0)20763 28988 y Fv(\270;)47 b Fc(e)-570 b Fv(!)22245 28618 y Fq(u;)221 b(u)p Fp(i)p Fr(,)6082 31579 y Fp(h)p Fq(V)7646 31030 y Fz(0)7357 31907 y Fv(\270;)47 b Fc(e)-570 b Fv(!)8839 31579 y Fq(u;)221 b(u)p Fp(i)1108 b Fr(=)15862 30317 y Fl(X)14644 33152 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)17135 32899 y Ff(0)17433 33152 y Fk(\267)p Fv(m)18997 31579 y Fp(h)p Fq(V)20561 31030 y Fz(0)20272 31907 y Fv(\270;)47 b Fc(e)-570 b Fv(!)21755 31579 y Fp(T)22602 31778 y Fc(e)-647 b Fv(')23091 31934 y Fi(\270;)p Fe(1)p Fi(;k)25054 31579 y Fr(\()p Fq(u)26300 31778 y Fv(k)26869 31579 y Fr(\))p Fq(;)221 b Fp(T)28804 31778 y Fc(e)-647 b Fv(')29293 32032 y Fi(\270;)p Fe(1)p Fi(;k)31145 31841 y Ff(0)31555 31579 y Fr(\()p Fq(u)32801 31778 y Fv(k)33315 31526 y Ff(0)33668 31579 y Fr(\))p Fp(i)34691 31834 y Fv(L)35331 31582 y Fe(2)35791 31834 y Fz(\()p Fj(R)36797 31582 y Fi(d)37279 31834 y Fz(\))12526 35294 y Fr(+)15862 34032 y Fl(X)14644 36867 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)17135 36615 y Ff(0)17433 36867 y Fk(\267)p Fv(m)18997 35294 y Fp(h)p Fq(V)20561 34746 y Fz(0)20272 35623 y Fv(\270;)47 b Fc(e)-570 b Fv(!)21755 35294 y Fp(T)22478 35493 y Fv(\261)157 b Fc(e)-647 b Fv(')23540 35649 y Fi(\270;)p Fe(1)p Fi(;k)25503 35294 y Fr(\()26009 34150 y Fl(p)p 27338 34150 1948 54 v 27338 35294 a Fq(\263)27906 35493 y Fv(k)24 b(;\270)29285 35294 y Fq(u)30025 35493 y Fv(k)30594 35294 y Fr(\))p Fq(;)221 b Fp(T)32405 35493 y Fv(\261)158 b Fc(e)-648 b Fv(')33467 35748 y Fi(\270;)p Fe(1)p Fi(;k)35319 35557 y Ff(0)35729 35294 y Fr(\()36235 34150 y Fl(p)p 37564 34150 2246 54 v 37564 35294 a Fq(\263)38132 35493 y Fv(k)38646 35241 y Ff(0)38943 35493 y Fv(;\270)39809 35294 y Fq(u)40549 35493 y Fv(k)41063 35241 y Ff(0)41416 35294 y Fr(\))p Fp(i)42439 35550 y Fv(L)43079 35298 y Fe(2)43540 35550 y Fz(\()p Fj(R)44546 35298 y Fi(d)45027 35550 y Fz(\))12526 39143 y Fr(+)1106 b(2)16733 37881 y Fl(X)15515 40716 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)18006 40464 y Ff(0)18305 40716 y Fk(\267)p Fv(m)20091 39143 y Fp(<)21050 37668 y Fl(\263)21843 39143 y Fp(h)p Fq(V)23407 38594 y Fz(0)23118 39471 y Fv(\270;)47 b Fc(e)-570 b Fv(!)24600 39143 y Fp(T)25447 39342 y Fc(e)-647 b Fv(')25936 39498 y Fi(\270;)p Fe(1)p Fi(;k)27900 39143 y Fr(\()p Fq(u)29146 39342 y Fv(k)29715 39143 y Fr(\))p Fq(;)221 b Fp(T)31526 39342 y Fv(\261)158 b Fc(e)-648 b Fv(')32588 39597 y Fi(\270;)p Fe(1)p Fi(;k)34440 39406 y Ff(0)34850 39143 y Fr(\()35356 37999 y Fl(p)p 36684 37999 V 1144 x Fq(\263)37252 39342 y Fv(k)37766 39090 y Ff(0)38064 39342 y Fv(;\270)38930 39143 y Fq(u)39670 39342 y Fv(k)40184 39090 y Ff(0)40537 39143 y Fr(\))p Fp(i)41560 39399 y Fv(L)42200 39146 y Fe(2)42661 39399 y Fz(\()p Fj(R)43667 39146 y Fi(d)44148 39399 y Fz(\))44569 37668 y Fl(\264)45363 39143 y Fq(:)4317 42967 y Fr(W)-108 b(e)434 b(start)f(b)-36 b(y)434 b(estimating)g(the)f (three)g(sums)g(of)h(the)f(last)h(equation.)4317 44572 y(F)-108 b(or)484 b(the)f(second)g(sum,)h(using)g(Cauc)-36 b(h)g(y)484 b(Sc)-36 b(h)g(w)g(artz)483 b(inequalit)-36 b(y)485 b(and)e(Lemma)h(3.2,)h(w)-36 b(e)4317 46177 y(get)434 b(that)f(for)h(an)-36 b(y)434 b(1)369 b Fp(\267)g Fq(k)45 b(;)221 b(k)18192 45695 y Fk(0)18873 46177 y Fp(\267)369 b Fq(m)p Fr(,)433 b(there)g(exists)i Fq(C)464 b(>)368 b Fr(0)434 b(suc)-36 b(h)433 b(that)g(w)-36 b(e)434 b(ha)-36 b(v)g(e,)5424 47791 y Fl(\257)5424 48588 y(\257)5424 49385 y(\257)5867 49318 y Fp(h)p Fq(V)7431 48770 y Fz(0)7142 49647 y Fv(\270;)47 b Fc(e)-570 b Fv(!)8624 49318 y Fp(T)9347 49517 y Fv(\261)158 b Fc(e)-648 b Fv(')10409 49673 y Fi(\270;)p Fe(1)p Fi(;k)12373 49318 y Fr(\()12879 48174 y Fl(p)p 14207 48174 1948 54 v 1144 x Fq(\263)14775 49517 y Fv(k)24 b(;\270)16154 49318 y Fq(u)16894 49517 y Fv(k)17463 49318 y Fr(\))p Fq(;)221 b Fp(T)19274 49517 y Fv(\261)158 b Fc(e)-648 b Fv(')20336 49772 y Fi(\270;)p Fe(1)p Fi(;k)22188 49581 y Ff(0)22599 49318 y Fr(\()23105 48174 y Fl(p)p 24433 48174 2246 54 v 1144 x Fq(\263)25001 49517 y Fv(k)25515 49266 y Ff(0)25813 49517 y Fv(;\270)26678 49318 y Fq(u)27418 49517 y Fv(k)27932 49266 y Ff(0)28286 49318 y Fr(\))p Fp(i)29309 49574 y Fv(L)29949 49322 y Fe(2)30409 49574 y Fz(\()p Fj(R)31415 49322 y Fi(d)31897 49574 y Fz(\))32318 47791 y Fl(\257)32318 48588 y(\257)32318 49385 y(\257)9506 52379 y Fp(\267)11908 51481 y Fr(1)p 11908 52074 651 54 v 11908 53291 a(2)12691 50905 y Fl(\263)13484 52379 y Fp(k)p Fq(V)15196 51831 y Fz(0)14906 52708 y Fv(\270;)47 b Fc(e)-570 b Fv(!)16389 52379 y Fp(T)17112 52578 y Fv(\261)158 b Fc(e)-648 b Fv(')18174 52734 y Fi(\270;)p Fe(1)p Fi(;k)20138 52379 y Fr(\()20644 51235 y Fl(p)p 21972 51235 1948 54 v 1144 x Fq(\263)22540 52578 y Fv(k)24 b(;\270)23919 52379 y Fq(u)24659 52578 y Fv(k)25228 52379 y Fr(\))p Fp(k)26398 51831 y Fz(2)26398 52757 y Fv(L)27038 52505 y Fe(2)27499 52757 y Fz(\()p Fj(R)28505 52505 y Fi(d)28987 52757 y Fz(\))29703 52379 y Fr(+)295 b Fp(kT)32397 52578 y Fv(\261)158 b Fc(e)-648 b Fv(')33459 52833 y Fi(\270;)p Fe(1)p Fi(;k)35311 52642 y Ff(0)35721 52379 y Fr(\()36227 51235 y Fl(p)p 37556 51235 2246 54 v 37556 52379 a Fq(\263)38124 52578 y Fv(k)38638 52326 y Ff(0)38935 52578 y Fv(;\270)39801 52379 y Fq(u)40541 52578 y Fv(k)41055 52326 y Ff(0)41408 52379 y Fr(\))p Fp(k)42578 51831 y Fz(2)42578 52757 y Fv(L)43218 52505 y Fe(2)43679 52757 y Fz(\()p Fj(R)44685 52505 y Fi(d)45167 52757 y Fz(\))45588 50905 y Fl(\264)12847 55842 y Fp(\267)369 b Fq(C)390 b Fp(\242)16235 54367 y Fl(\263)17028 55842 y Fp(h)p Fq(\263)18113 56041 y Fv(k)24 b(;\270)19492 55842 y Fq(u)20232 56041 y Fv(k)20801 55842 y Fq(;)221 b(u)22123 56041 y Fv(k)22693 55842 y Fp(i)23210 56064 y Fv(L)23850 55812 y Fe(2)24310 56064 y Fz(\()p Fj(T)25266 55812 y Ff(\244)25746 56064 y Fz(\))26463 55842 y Fr(+)295 b Fp(h)p Fq(\263)28855 56041 y Fv(k)29369 55789 y Ff(0)29666 56041 y Fv(;\270)30532 55842 y Fq(u)31272 56041 y Fv(k)31786 55789 y Ff(0)32139 55842 y Fq(;)221 b(u)33461 56041 y Fv(k)33975 55789 y Ff(0)34329 55842 y Fp(i)34846 56064 y Fv(L)35486 55812 y Fe(2)35947 56064 y Fz(\()p Fj(T)36903 55812 y Ff(\244)37383 56064 y Fz(\))37804 54367 y Fl(\264)38597 55842 y Fq(:)4317 58280 y Fr(So)434 b(there)f(exists)h Fq(C)464 b(>)368 b Fr(0)434 b(suc)-36 b(h)433 b(that)g(w)-36 b(e)434 b(ha)-36 b(v)g(e)6863 59868 y Fl(X)5645 62703 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)8136 62450 y Ff(0)8434 62703 y Fk(\267)p Fv(m)10220 59602 y Fl(\257)10220 60399 y(\257)10220 61196 y(\257)10663 61130 y Fp(h)p Fq(V)12227 60581 y Fz(0)11938 61458 y Fv(\270;)47 b Fc(e)-570 b Fv(!)13420 61130 y Fp(T)14143 61329 y Fv(\261)158 b Fc(e)-648 b Fv(')15205 61485 y Fi(\270;)p Fe(1)p Fi(;k)17169 61130 y Fr(\()17675 59985 y Fl(p)p 19003 59985 1948 54 v 1145 x Fq(\263)19571 61329 y Fv(k)24 b(;\270)20950 61130 y Fq(u)21690 61329 y Fv(k)22259 61130 y Fr(\))p Fq(;)221 b Fp(T)24070 61329 y Fv(\261)158 b Fc(e)-648 b Fv(')25132 61583 y Fi(\270;)p Fe(1)p Fi(;k)26984 61392 y Ff(0)27395 61130 y Fr(\()27901 59985 y Fl(p)p 29229 59985 2246 54 v 1145 x Fq(\263)29797 61329 y Fv(k)30311 61077 y Ff(0)30609 61329 y Fv(;\270)31474 61130 y Fq(u)32214 61329 y Fv(k)32728 61077 y Ff(0)33082 61130 y Fr(\))p Fp(i)34105 61385 y Fv(L)34745 61133 y Fe(2)35205 61385 y Fz(\()p Fj(R)36211 61133 y Fi(d)36693 61385 y Fz(\))37114 59602 y Fl(\257)37114 60399 y(\257)37114 61196 y(\257)30586 64845 y Fp(\267)369 b Fq(C)33916 63583 y Fl(X)33235 66412 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)36515 64845 y Fp(h)p Fq(\263)37600 65044 y Fv(k)g(;\270)38979 64845 y Fq(u)39719 65044 y Fv(k)40288 64845 y Fq(;)221 b(u)41610 65044 y Fv(k)42180 64845 y Fp(i)p Fq(:)1107 b Fr(\(3.15\))25253 70015 y(12)p eop end %%Page: 13 13 TeXDict begin 13 12 bop 4317 7306 a Fr(F)-108 b(or)446 b(the)h(third)e(sum,)i(using)g(the)f(Cauc)-36 b(h)g(y-Sc)g(h)g(w)g (artz)446 b(inequalit)-36 b(y)447 b(once)g(more,)g(w)-36 b(e)447 b(get)4317 8911 y(that)433 b(for)h(1)370 b Fp(\267)f Fq(k)414 b Fp(\267)369 b Fq(m)p Fr(,)434 b(there)e(exists)j Fq(\257)443 b(>)368 b Fr(0)434 b(suc)-36 b(h)433 b(that)g(w)-36 b(e)434 b(ha)-36 b(v)g(e)5424 10676 y Fl(\257)5424 11473 y(\257)5424 12270 y(\257)5867 12204 y Fp(h)p Fq(V)7431 11655 y Fz(0)7142 12532 y Fv(\270;)47 b Fc(e)-570 b Fv(!)8624 12204 y Fp(T)9471 12403 y Fc(e)-647 b Fv(')9960 12559 y Fi(\270;)p Fe(1)p Fi(;k)11923 12204 y Fr(\()p Fq(u)13169 12403 y Fv(k)13738 12204 y Fr(\))p Fq(;)221 b Fp(T)15549 12403 y Fv(\261)158 b Fc(e)-648 b Fv(')16611 12657 y Fi(\270;)p Fe(1)p Fi(;k)18463 12466 y Ff(0)18874 12204 y Fr(\()19380 11060 y Fl(p)p 20708 11060 2246 54 v 1144 x Fq(\263)21276 12403 y Fv(k)21790 12151 y Ff(0)22088 12403 y Fv(;\270)22953 12204 y Fq(u)23693 12403 y Fv(k)24207 12151 y Ff(0)24561 12204 y Fr(\))p Fp(i)25584 12459 y Fv(L)26224 12207 y Fe(2)26684 12459 y Fz(\()p Fj(R)27690 12207 y Fi(d)28172 12459 y Fz(\))28593 10676 y Fl(\257)28593 11473 y(\257)28593 12270 y(\257)9303 14760 y Fp(\267)369 b Fq(\257)74 b Fp(k)p Fq(V)13224 14212 y Fz(0)12982 15088 y Fc(e)-570 b Fv(!)13750 14760 y Fp(T)14597 14959 y Fc(e)-647 b Fv(')15086 15115 y Fi(\270;)p Fe(1)p Fi(;k)17049 14760 y Fr(\()p Fq(u)18295 14959 y Fv(k)18864 14760 y Fr(\))p Fp(k)20034 14212 y Fz(2)20034 15138 y Fv(L)20674 14885 y Fe(2)21135 15138 y Fz(\()p Fj(R)22141 14885 y Fi(d)22623 15138 y Fz(\))23339 14760 y Fr(+)295 b(1)p Fq(=)p Fr(\(4)p Fq(\257)74 b Fr(\))p Fp(kT)29803 14959 y Fv(\261)158 b Fc(e)-648 b Fv(')30865 15214 y Fi(\270;)p Fe(1)p Fi(;k)32717 15023 y Ff(0)33128 14760 y Fr(\()33634 13616 y Fl(p)p 34962 13616 1948 54 v 1144 x Fq(\263)35530 14959 y Fv(k)24 b(;\270)36909 14760 y Fq(u)37649 14959 y Fv(k)38163 14707 y Ff(0)38516 14760 y Fr(\))p Fp(k)39686 14212 y Fz(2)39686 15138 y Fv(L)40326 14885 y Fe(2)40788 15138 y Fz(\()p Fj(R)41794 14885 y Fi(d)42275 15138 y Fz(\))42696 14760 y Fq(:)1108 b Fr(\(3.16\))4317 17829 y(Using)434 b(equation)g (\(3.11\),)h(one)e(gets)h(that)f(there)g(exist)31941 17493 y Fl(e)31688 17829 y Fq(C)32619 18028 y Fz(1)33145 17829 y Fq(;)33980 17493 y Fl(e)33727 17829 y Fq(C)34658 18028 y Fz(2)35553 17829 y Fq(>)368 b Fr(0)434 b(suc)-36 b(h)433 b(that)6863 19933 y Fl(X)5645 22768 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)8136 22516 y Ff(0)8434 22768 y Fk(\267)p Fv(m)10220 19667 y Fl(\257)10220 20464 y(\257)10220 21261 y(\257)10663 21195 y Fp(h)p Fq(V)12227 20646 y Fz(0)11938 21523 y Fv(\270;)47 b Fc(e)-570 b Fv(!)13420 21195 y Fp(T)14267 21394 y Fc(e)-647 b Fv(')14756 21550 y Fi(\270;)p Fe(1)p Fi(;k)16719 21195 y Fr(\()p Fq(u)17965 21394 y Fv(k)18534 21195 y Fr(\))p Fq(;)221 b Fp(T)20345 21394 y Fv(\261)158 b Fc(e)-648 b Fv(')21407 21649 y Fi(\270;)p Fe(1)p Fi(;k)23259 21458 y Ff(0)23670 21195 y Fr(\()24176 20051 y Fl(p)p 25504 20051 2246 54 v 1144 x Fq(\263)26072 21394 y Fv(k)26586 21142 y Ff(0)26884 21394 y Fv(;\270)27749 21195 y Fq(u)28489 21394 y Fv(k)29003 21142 y Ff(0)29357 21195 y Fr(\))p Fp(i)30380 21451 y Fv(L)31020 21199 y Fe(2)31480 21451 y Fz(\()p Fj(R)32486 21199 y Fi(d)32968 21451 y Fz(\))33389 19667 y Fl(\257)33389 20464 y(\257)33389 21261 y(\257)5886 24911 y Fp(\267)7541 24575 y Fl(e)7288 24911 y Fq(C)8219 25110 y Fz(1)8745 24911 y Fq(\257)10455 23649 y Fl(X)9774 26478 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)13434 23649 y Fl(X)13275 26576 y Fv(\260)52 b Fk(2)p Fj(Z)15029 26324 y Fi(d)15793 24911 y Fl(e)-798 b Fq(!)16543 25110 y Fv(\260)17135 24911 y Fp(j)330 b Fr(^)-980 b Fq(u)18244 25110 y Fv(k)18814 24911 y Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)20942 24362 y Fz(2)21762 24911 y Fr(+)23321 24575 y Fl(e)23069 24911 y Fq(C)24000 25110 y Fz(2)24525 24911 y Fr(\()p Fq(\257)369 b Fr(+)295 b(1)p Fq(=\257)74 b Fr(\))30957 23649 y Fl(X)30276 26478 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)33557 24911 y Fp(h)p Fq(\263)34642 25110 y Fv(\270;k)36021 24911 y Fq(u)36761 25110 y Fv(k)37330 24911 y Fq(;)221 b(u)38652 25110 y Fv(k)39221 24911 y Fp(i)39738 25133 y Fv(L)40378 24881 y Fe(2)40839 25133 y Fz(\()p Fj(T)41795 24881 y Ff(\244)42275 25133 y Fz(\))42696 24911 y Fq(:)1108 b Fr(\(3.17\))4317 29052 y(F)-108 b(or)433 b(the)g(\257rst)g(sum,)g (using)h(\(3.10\),)h(w)-36 b(e)434 b(get)f(that)g(there)g(exist)i Fq(C)36534 28570 y Fk(0)36439 29380 y Fz(1)36964 29052 y Fq(;)221 b(C)38572 28570 y Fk(0)38477 29380 y Fz(2)39372 29052 y Fq(>)369 b Fr(0)433 b(suc)-36 b(h)433 b(that)5424 30891 y Fl(\257)5424 31688 y(\257)5424 32485 y(\257)7305 31156 y(X)6088 33991 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)8579 33739 y Ff(0)8877 33991 y Fk(\267)p Fv(m)10441 32418 y Fp(h)p Fq(V)12005 31870 y Fz(0)11763 32747 y Fc(e)-570 b Fv(!)12531 32418 y Fp(T)13378 32617 y Fc(e)-647 b Fv(')13867 32773 y Fi(\270;)p Fe(1)p Fi(;k)15830 32418 y Fr(\()p Fq(u)17076 32617 y Fv(k)17645 32418 y Fr(\))p Fq(;)221 b Fp(T)19580 32617 y Fc(e)-647 b Fv(')20069 32872 y Fi(\270;)p Fe(1)p Fi(;k)21921 32681 y Ff(0)22331 32418 y Fr(\()p Fq(u)23577 32617 y Fv(k)24091 32365 y Ff(0)24444 32418 y Fr(\))p Fp(i)25467 32674 y Fv(L)26107 32422 y Fe(2)26568 32674 y Fz(\()p Fj(R)27574 32422 y Fi(d)28055 32674 y Fz(\))11143 36547 y Fp(\241)13688 35285 y Fl(X)12471 38120 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)14962 37868 y Ff(0)15260 38120 y Fk(\267)p Fv(m)17204 35285 y Fl(X)17046 38213 y Fv(\260)52 b Fk(2)p Fj(Z)18800 37960 y Fi(d)19563 36547 y Fl(e)-797 b Fq(!)20314 36746 y Fv(\260)20906 35471 y Fl(\241)21736 34739 y(Z)22474 37746 y Fv(C)23145 37869 y Fe(0)23882 36547 y Fq(a)24565 36746 y Fv(')25178 36902 y Fi(\270;)p Fe(1)26381 36746 y Fv(;k)24 b(;k)27931 36494 y Ff(0)28284 36547 y Fr(\()p Fq(x)p Fr(\))p Fq(dx)31450 35471 y Fl(\242)32059 36547 y Fr(\()329 b(^)-979 b Fq(u)33305 36746 y Fv(k)33874 36547 y Fr(\)\()p Fq(\260)72 b Fr(\))p 36139 35392 4378 54 v(\()477 b(^)-1127 b Fq(u)37385 36746 y Fv(k)37899 36494 y Ff(0)38251 36547 y Fr(\)\()p Fq(\260)72 b Fr(\))40515 35020 y Fl(\257)40515 35817 y(\257)40515 36614 y(\257)6044 40355 y Fp(\267)369 b Fq(C)8472 39807 y Fk(0)8377 40684 y Fz(1)8902 40355 y Fq(\257)10612 39093 y Fl(X)9932 41922 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)13592 39093 y Fl(X)13433 42021 y Fv(\260)52 b Fk(2)p Fj(Z)15187 41768 y Fi(d)15951 40355 y Fl(e)-798 b Fq(!)16701 40554 y Fv(\260)17293 40355 y Fp(j)329 b Fr(^)-979 b Fq(u)18402 40554 y Fv(k)18971 40355 y Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)21099 39807 y Fz(2)21920 40355 y Fr(+)295 b Fq(C)24253 39807 y Fk(0)24158 40684 y Fz(2)24683 40355 y Fr(\(1)g(+)g(1)p Fq(=\257)74 b Fr(\))30957 39093 y Fl(X)30276 41922 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)33557 40355 y Fp(h)p Fq(\263)34642 40554 y Fv(\270;k)36021 40355 y Fq(u)36761 40554 y Fv(k)37330 40355 y Fq(;)221 b(u)38652 40554 y Fv(k)39221 40355 y Fp(i)39738 40578 y Fv(L)40378 40326 y Fe(2)40839 40578 y Fz(\()p Fj(T)41795 40326 y Ff(\244)42275 40578 y Fz(\))42696 40355 y Fq(:)1108 b Fr(\(3.18\))4317 44496 y(No)-36 b(w)357 b(equations)f(\(3.15\),)i (\(3.17\))f(and)e(\(3.18\))i(giv)-36 b(e)357 b(that)f(there)f(exist)i Fq(K)39492 44695 y Fz(1)40017 44496 y Fq(;)221 b(K)41706 44695 y Fz(2)42601 44496 y Fq(>)369 b Fr(0)356 b(suc)-36 b(h)4317 46101 y(that)5424 47888 y Fl(\257)5424 48686 y(\257)5424 49483 y(\257)5867 49416 y Fp(h)p Fq(V)7431 48868 y Fz(0)7142 49745 y Fv(\270;)47 b Fc(e)-570 b Fv(!)8624 49416 y Fq(u;)221 b(u)p Fp(i)296 b(\241)14045 48154 y Fl(X)12827 50989 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)15318 50737 y Ff(0)15616 50989 y Fk(\267)p Fv(m)17561 48154 y Fl(X)17402 51081 y Fv(\260)52 b Fk(2)p Fj(Z)19156 50829 y Fi(d)19920 49416 y Fl(e)-798 b Fq(!)20670 49615 y Fv(\260)21262 47942 y Fl(\263)22277 47608 y(Z)23015 50615 y Fv(C)23686 50738 y Fe(0)24423 49416 y Fq(a)25106 49615 y Fv(')25719 49771 y Fi(\270;)p Fe(1)26922 49615 y Fv(;k)24 b(;k)28472 49363 y Ff(0)28825 49416 y Fr(\()p Fq(x)p Fr(\))p Fq(dx)31991 47942 y Fl(\264)32784 49416 y Fr(\()329 b(^)-979 b Fq(u)34030 49615 y Fv(k)34599 49416 y Fr(\)\()p Fq(\260)72 b Fr(\))p 36864 48260 V(\()478 b(^)-1128 b Fq(u)38110 49615 y Fv(k)38624 49363 y Ff(0)38977 49416 y Fr(\)\()p Fq(\260)72 b Fr(\))41241 47888 y Fl(\257)41241 48686 y(\257)41241 49483 y(\257)42053 49416 y Fp(\267)6082 53224 y Fq(K)7189 53423 y Fz(1)7715 53224 y Fq(\257)9425 51962 y Fl(X)8744 54791 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)12404 51962 y Fl(X)12245 54889 y Fv(\260)52 b Fk(2)p Fj(Z)13999 54637 y Fi(d)14763 53224 y Fl(e)-798 b Fq(!)15513 53423 y Fv(\260)16105 53224 y Fp(j)p Fr(\()330 b(^)-980 b Fq(u)17720 53423 y Fv(k)18289 53224 y Fr(\)\()p Fq(\260)72 b Fr(\))p Fp(j)20923 52676 y Fz(2)21744 53224 y Fr(+)295 b Fq(K)24158 53423 y Fz(2)24683 53224 y Fr(\(1)g(+)g(1)p Fq(=\257)74 b Fr(\))30957 51962 y Fl(X)30276 54791 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)33557 53224 y Fp(h)p Fq(\263)34642 53423 y Fv(k)g(;\270)36021 53224 y Fq(u)36761 53423 y Fv(k)37330 53224 y Fq(;)221 b(u)38652 53423 y Fv(k)39221 53224 y Fp(i)39738 53447 y Fv(L)40378 53195 y Fe(2)40839 53447 y Fz(\()p Fj(T)41795 53195 y Ff(\244)42275 53447 y Fz(\))42696 53224 y Fq(:)1108 b Fr(\(3.19\))4317 57291 y(No)-36 b(w,)435 b(if)f(the)f(matrix)15605 60532 y Fq(A)p Fr(\(0\))369 b(=)19992 59058 y Fl(\263)21007 58724 y(Z)21745 61732 y Fv(C)22416 61855 y Fe(0)23153 60532 y Fq(a)23836 60731 y Fv(')24449 60854 y Fe(0)p Fi(;)p Fe(1)25568 60731 y Fv(;k)24 b(;k)27118 60479 y Ff(0)27472 60532 y Fr(\()p Fq(x)p Fr(\))p Fq(dx)30638 59058 y Fl(\264)31431 61451 y Fz(1)p Fk(\267)p Fv(k)g(;k)33922 61199 y Ff(0)34220 61451 y Fk(\267)p Fv(m)35839 60532 y Fq(;)4317 64025 y Fr(is)434 b(p)36 b(ositiv)-36 b(e-de\257nite,)433 b(one)h(gets)g (that)f(inf)314 b Fq(\276)48 b Fr(\()p Fq(A)p Fr(\(0\)\))369 b(=)f Fq(C)464 b(>)369 b Fr(0)434 b(satis\257es)23106 66694 y Fq(C)95 b(I)24706 66893 y Fv(m)25962 66694 y Fp(\267)369 b Fq(A:)25253 70015 y Fr(13)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 4317 7306 a Fr(Let)433 b Fq(A)p Fr(\()p Fq(\270)p Fr(\))g(b)36 b(e)434 b(the)f(matrix,)17757 9411 y Fl(\263)18772 9077 y(Z)19510 12084 y Fv(C)20181 12207 y Fe(0)20918 10885 y Fq(a)21601 11084 y Fv(')22214 11240 y Fi(\270;)p Fe(1)23417 11084 y Fv(;k)24 b(;k)24967 10832 y Ff(0)25320 10885 y Fr(\()p Fq(x)p Fr(\))p Fq(dx)28486 9411 y Fl(\264)29279 11804 y Fz(1)p Fk(\267)p Fv(k)g(;k)31770 11552 y Ff(0)32068 11804 y Fk(\267)p Fv(m)33687 10885 y Fq(:)4317 14620 y Fr(Notice)434 b(that)f(for)i(an)-36 b(y)433 b(1)370 b Fp(\267)f Fq(k)45 b(;)221 b(k)20107 14138 y Fk(0)20787 14620 y Fp(\267)369 b Fq(m)p Fr(,)434 b(the)f(functions)16047 18126 y Fq(f)16688 18325 y Fv(k)24 b(;k)17977 18073 y Ff(0)18699 18126 y Fr(:)370 b Fq(\270)e Fp(!)22255 16318 y Fl(Z)22993 19325 y Fv(C)23664 19448 y Fe(0)24401 18126 y Fq(a)25084 18332 y Fv(')25697 18488 y Fi(\270;)p Fe(1)26899 18332 y Fv(;\265)27599 18488 y Fi(k)28108 18332 y Fz(\()p Fv(\270)p Fz(\))p Fv(;\265)30089 18587 y Fi(k)30542 18396 y Ff(0)30895 18332 y Fz(\()p Fv(\270)p Fz(\))32231 18126 y Fr(\()p Fq(x)p Fr(\))p Fq(dx;)4317 21883 y Fr(are)434 b(con)-36 b(tin)g(uous)432 b(in)i Fq(\270)p Fr(.)f(So)h(there)f(exists)h Fq(\270)25547 22082 y Fz(0)26442 21883 y Fq(>)368 b Fr(0)434 b(suc)-36 b(h)433 b(that)g(for)h(an)-36 b(y)434 b Fq(\270)369 b Fp(2)f Fr([0)p Fq(;)221 b(\270)43836 22082 y Fz(0)44363 21883 y Fr(])22220 24562 y Fq(C)p 22220 25155 1026 54 v 22408 26372 a Fr(2)23379 25461 y Fq(I)23953 25660 y Fv(m)25209 25461 y Fp(\267)370 b Fq(A)p Fr(\()p Fq(\270)p Fr(\))p Fq(:)4317 28864 y Fr(This)434 b(giv)-36 b(es)435 b(that)e(for)h(an)-36 b(y)434 b Fq(u)369 b Fp(2)f Fq(L)20984 28382 y Fz(2)21510 28864 y Fr(\()p Fm(T)22902 28382 y Fk(\244)23427 28864 y Fr(\))5557 31875 y Fq(C)p 5557 32468 V 5745 33685 a Fr(2)7618 31511 y Fl(X)6937 34340 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)10597 31511 y Fl(X)10438 34439 y Fv(\260)52 b Fk(2)p Fj(Z)12192 34187 y Fi(d)12956 32773 y Fl(e)-798 b Fq(!)13706 32972 y Fv(\260)14299 32773 y Fp(j)p Fr(\()329 b(^)-979 b Fq(u)15914 32972 y Fv(k)16483 32773 y Fr(\)\()p Fq(\260)72 b Fr(\))p Fp(j)19117 32225 y Fz(2)12881 36995 y Fp(\267)15500 35733 y Fl(X)14283 38568 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)16774 38316 y Ff(0)17072 38568 y Fk(\267)p Fv(m)19016 35733 y Fl(X)18857 38660 y Fv(\260)52 b Fk(2)p Fj(Z)20611 38408 y Fi(d)21375 36995 y Fl(e)-797 b Fq(!)22126 37194 y Fv(\260)22718 35520 y Fl(\263)23732 35187 y(Z)24470 38194 y Fv(C)25141 38317 y Fe(0)25879 36995 y Fq(a)26562 37194 y Fv(')27175 37350 y Fi(\270;)p Fe(1)28377 37194 y Fv(;k)24 b(;k)29927 36942 y Ff(0)30280 36995 y Fr(\()p Fq(x)p Fr(\))p Fq(dx)33446 35520 y Fl(\264)34240 36995 y Fr(\()329 b(^)-979 b Fq(u)35486 37194 y Fv(k)36054 36995 y Fr(\)\()p Fq(\260)72 b Fr(\))p 38319 35839 4378 54 v(\()478 b(^)-1128 b Fq(u)39565 37194 y Fv(k)40079 36942 y Ff(0)40432 36995 y Fr(\)\()p Fq(\260)72 b Fr(\))o Fq(:)1108 b Fr(\(3.20\))4317 41457 y(No)-36 b(w)341 b(using)f(the)g(expanation)g(of)h Fp(h)p Fq(V)22185 40975 y Fz(0)21896 41827 y Fv(\270;)47 b Fc(e)-570 b Fv(!)23379 41457 y Fq(u;)221 b(u)p Fp(i)341 b Fr(and)e(equation)i (\(3.19\),)h(w)-36 b(e)340 b(get)g(that)g(there)4317 43062 y(exist)434 b Fq(K)8502 43261 y Fz(1)9028 43062 y Fq(;)221 b(K)10717 43261 y Fz(2)11612 43062 y Fq(>)368 b Fr(0)434 b(and)f Fq(\257)443 b(>)369 b 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Fz(2)27393 60042 y Fp(\241)295 b Fq(C)29652 60241 y Fz(2)31080 58780 y Fl(X)30399 61609 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)33679 60042 y Fp(h)p Fq(\263)34764 60241 y Fv(k)g(;\270)36143 60042 y Fq(u)36883 60241 y Fv(k)37452 60042 y Fq(;)221 b(u)38774 60241 y Fv(k)39344 60042 y Fp(i)39861 60264 y Fv(L)40501 60012 y Fe(2)40962 60264 y Fz(\()p Fj(T)41918 60012 y Ff(\244)42398 60264 y Fz(\))42819 60042 y Fq(:)985 b Fr(\(3.22\))4317 64374 y(This)434 b(ends)f(the)g(pro)36 b(of)434 b(of)g(Prop)36 b(osition)434 b(3.5.)20061 b Fa(\244)25253 70015 y Fr(14)p eop end %%Page: 15 15 TeXDict begin 15 14 bop 4317 7306 a Fd(3.2)1793 b(If)597 b Fb(A)p FB(\(0\))i Fd(is)f(negativ)-50 b(e-de\257nite)4317 9769 y Fr(Let)433 b Fq(H)7725 9988 y Fv(\270;!)9152 9736 y Fe(+)10317 9769 y Fr(b)36 b(e)434 b(the)f(follo)-36 b(wing)435 b(op)36 b(erator,)14452 12994 y Fq(H)15530 13213 y Fv(\270;!)16957 12961 y Fe(+)18057 12994 y Fr(=)369 b Fp(\241)p Fr(\242)295 b(+)g Fq(W)24385 13193 y Fz(p)26 b(er)26069 12994 y Fr(+)295 b Fq(\270)28515 11732 y Fl(X)28356 14659 y Fv(\260)52 b Fk(2)p Fj(Z)30110 14407 y Fi(d)30814 12994 y Fq(!)31672 12445 y Fz(+)32459 12994 y Fq(f)142 b Fr(\()p Fp(\242)295 b(\241)g Fq(\260)72 b Fr(\))p Fq(:)4317 17500 y Fr(As)496 b Fq(H)7379 17719 y Fv(\270;!)8806 17467 y Fe(+)10033 17500 y Fr(is)h(a)f Fm(Z)13436 17018 y Fv(d)13975 17500 y Fr(-p)36 b(erio)g(dic)496 b(op)36 b(erator,)496 b(the)f(analysis)j(giv)-36 b(en)496 b(in)g(subsection)f (2.1)i(for)4317 19105 y Fq(H)5395 19324 y Fv(\270;!)6822 19072 y Fe(+)8013 19105 y Fr(is)460 b(still)h(true)e(in)g(the)h(presen) -36 b(t)458 b(case.)j(F)-108 b(or)459 b(\()p Fq(E)30007 19304 y Fv(j)30494 19105 y Fr(\()p Fq(\270;)221 b(\265)36 b Fr(\)\))33995 19304 y Fv(j)51 b Fk(2)p Fj(N)35694 19053 y Ff(\244)36228 19105 y Fr(,)460 b(the)f(Flo)36 b(quet)461 b(eigen-)4317 20711 y(v)-72 b(alue)434 b(of)h Fq(H)10237 20929 y Fv(\270;!)11664 20677 y Fe(+)12829 20711 y Fr(let)e(us)h(set)f Fq(E)19370 20929 y Fv(\270;!)20797 20677 y Fe(+)21898 20711 y Fr(=)368 b(inf)24852 20910 y Fv(\265)26 b Fk(2)p Fj(T)26534 20658 y Ff(\244)27291 20711 y Fq(E)28254 20910 y Fz(1)28780 20711 y Fr(\()p Fq(\270;)221 b(\265)36 b Fr(\).)4317 23423 y FA(Theorem)499 b(3.7)651 b Fg(Assume)435 b(that)f(the)g(matrix)g Fq(A)p Fr(\(0\))g Fg(is)h(ne)-66 b(gative-de\257nite.)430 b(Then)k(ther)-66 b(e)4317 25028 y(exists)465 b Fq(\270)8630 25227 y Fz(0)9524 25028 y Fq(>)369 b Fr(0)465 b Fg(such)h(that)e(for)h(any)f Fq(\270)369 b Fp(2)g Fr([0)p Fq(;)221 b(\270)26933 25227 y Fz(0)27460 25028 y Fr(])465 b Fg(we)g(have:)12089 28326 y Fr(\246)13064 28525 y Fv(\270;)p Fz(0)14400 26852 y Fl(\263)15193 28326 y Fq(H)16271 28525 y Fv(\270;!)18049 28326 y Fp(\241)295 b Fq(E)20340 28545 y Fv(\270;!)21767 28293 y Fe(+)22499 26852 y Fl(\264)23292 28326 y Fr(\246)24267 28525 y Fv(\270;)p Fz(0)26998 28326 y Fg(is)465 b(a)930 b(p)-66 b(ositive)463 b(op)-66 b(er)g(ator.)4317 31551 y Fr(The)353 b(result)g(of)g(Theorem)h (3.7)f(can)g(b)36 b(e)353 b(pro)-36 b(v)g(ed)353 b(in)g(the)f(same)h(w) -36 b(a)g(y)354 b(as)f(w)-36 b(e)354 b(did)e(for)i(Theo-)4317 33156 y(rem)314 b(1.3)h(in)f(the)g(previous)g(subsection.)h(Indeed,)f Fq(H)29439 33355 y Fv(\270;!)31235 33156 y Fr(can)g(b)36 b(e)314 b(seen)g(as)g(a)h(p)36 b(erturbation)4317 34762 y(of)434 b Fq(H)6876 34980 y Fv(\270;!)8303 34728 y Fe(+)9469 34762 y Fr(as)f(follo)-36 b(w,)20433 36367 y Fq(H)21511 36566 y Fv(\270;!)23362 36367 y Fr(=)369 b Fq(H)25821 36586 y Fv(\270;!)27248 36333 y Fe(+)28274 36367 y Fr(+)295 b Fq(V)p 30339 36065 673 40 v 199 x Fv(!)31012 36367 y Fq(:)4317 38983 y Fr(With)436 b Fq(V)p 8437 38681 V 199 x Fv(!)9109 38983 y Fr(\()p Fp(\242)p Fr(\))372 b(=)12405 37721 y Fl(X)12246 40648 y Fv(\260)52 b Fk(2)p Fj(Z)14000 40396 y Fi(d)p 14704 38251 858 54 v 14704 38983 a Fq(!)15562 39182 y Fv(\260)16154 38983 y Fq(f)142 b Fr(\()p Fp(\242)296 b(\241)h Fq(\260)72 b Fr(\))435 b(and)h(for)g(an)-36 b(y)436 b Fq(\260)444 b Fp(2)372 b Fm(Z)31369 38501 y Fv(d)p 32343 38251 V 32343 38983 a Fq(!)33201 39182 y Fv(\260)34166 38983 y Fr(=)g Fq(!)36360 39182 y Fv(\260)37248 38983 y Fp(\241)297 b Fq(!)39436 38501 y Fz(+)40223 38983 y Fr(.)436 b(Notice)g(that)4317 42060 y(in)e(this)f(case)h(\()p 11630 41329 V Fq(!)12487 42259 y Fv(\260)13080 42060 y Fr(\))13586 42316 y Fv(\260)52 b Fk(2)p Fj(Z)15340 42064 y Fi(d)16311 42060 y Fr(is)434 b(a)g(family)h(of)f(b)36 b(ounded)432 b(and)h(negativ)-36 b(e)435 b(random)e(v)-72 b(ariables.)4317 43665 y(using)535 b(the)f(analogous)i(unitary)f (transformation,)h(one)f(gets)g(that)f Fq(H)39649 43183 y Fz(0)39546 44011 y Fv(\270;!)41563 43665 y Fr(is)h(unitarly)4317 45270 y(equiv)-72 b(alen)-36 b(t)434 b(to)20357 46875 y Fq(h)21106 46327 y Fz(0)21106 47204 y Fv(\270;!)22957 46875 y Fr(=)368 b Fq(h)25086 46327 y Fz(0)25086 47216 y Fv(\270;!)26513 46964 y Fe(+)27540 46875 y Fr(+)295 b Fq(V)29894 46327 y Fz(0)29605 47204 y Fv(\270;)p 30415 46703 617 40 v(!)31088 46875 y Fq(:)4317 49200 y Fr(The)301 b(lo)-36 b(w)g(er)302 b(b)36 b(ound)300 b(of)h Fq(h)16097 49419 y Fv(\270;!)17524 49167 y Fe(+)18557 49200 y Fr(can)g(b)36 b(e)301 b(deriv)-36 b(ed)300 b(easily)-108 b(.)303 b(As)e(all)h (argumen)-36 b(ts)301 b(used)f(to)h(lo)-36 b(w)g(er)4317 50805 y(b)36 b(ound)547 b Fq(V)9490 50323 y Fz(0)9247 51175 y Fc(e)-570 b Fv(!)10564 50805 y Fr(remain)548 b(v)-72 b(alid;)550 b(w)-36 b(e)548 b(lo)-36 b(w)g(er)549 b(b)36 b(ound)547 b Fq(V)29347 50323 y Fz(0)29057 51151 y Fv(\270;)p 29867 50650 V(!)31088 50805 y Fr(using)h(the)g(same)h (computation)4317 52410 y(done)433 b(in)h(subsection)f(3.1.)4317 54015 y(So)h(w)-36 b(e)433 b(get)h(that)f(there)g(exist)i Fq(K)20534 54214 y Fz(1)21059 54015 y Fq(;)221 b(K)22748 54214 y Fz(2)23643 54015 y Fq(>)369 b Fr(0)433 b(suc)-36 b(h)433 b(that)5424 56325 y Fl(\257)5424 57122 y(\257)5424 57919 y(\257)5867 57853 y Fp(h)p Fq(V)7431 57304 y Fz(0)7142 58181 y Fv(\270;)p 7952 57680 V(!)8624 57853 y Fq(u;)221 b(u)p Fp(i)296 b(\241)14045 56591 y Fl(X)12827 59426 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)15318 59174 y Ff(0)15616 59426 y Fk(\267)p Fv(m)17561 56591 y Fl(X)17402 59518 y Fv(\260)52 b Fk(2)p Fj(Z)19156 59266 y Fi(d)p 19860 57121 858 54 v 19860 57853 a Fq(!)20718 58052 y Fv(\260)21310 56378 y Fl(\263)22325 56045 y(Z)23062 59052 y Fv(C)23733 59175 y Fe(0)24471 57853 y Fq(a)25154 58052 y Fv(')25767 58208 y Fi(\270;)p Fe(1)26969 58052 y Fv(;k)24 b(;k)28519 57800 y Ff(0)28873 57853 y Fr(\()p Fq(x)p Fr(\))p Fq(dx)32039 56378 y Fl(\264)32832 57853 y Fr(\()329 b(^)-979 b Fq(u)34078 58052 y Fv(k)34647 57853 y Fr(\)\()p Fq(\260)72 b Fr(\))p 36912 56697 4378 54 v(\()477 b(^)-1127 b Fq(u)38158 58052 y Fv(k)38672 57800 y Ff(0)39024 57853 y Fr(\)\()p Fq(\260)72 b Fr(\))41289 56325 y Fl(\257)41289 57122 y(\257)41289 57919 y(\257)42100 57853 y Fp(\267)4884 61661 y Fq(K)5991 61860 y Fz(1)6516 61661 y Fq(\257)i Fr(\()p Fq(!)8688 61112 y Fz(+)9770 61661 y Fp(\241)295 b Fq(!)11956 61112 y Fk(\241)12743 61661 y Fr(\))14151 60399 y Fl(X)13470 63228 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)17130 60399 y Fl(X)16971 63326 y Fv(\260)52 b Fk(2)p Fj(Z)18725 63074 y Fi(d)19429 61661 y Fp(j)p Fr(\()330 b(^)-980 b Fq(u)21044 61860 y Fv(k)21613 61661 y Fr(\)\()p Fq(\260)72 b Fr(\))p Fp(j)24247 61112 y Fz(2)25068 61661 y Fr(+)294 b Fq(K)27481 61860 y Fz(2)28007 61661 y Fr(\(1)h(+)g(1)p Fq(=\257)74 b Fr(\))34281 60399 y Fl(X)33600 63228 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)36881 61661 y Fp(h)p Fq(\263)37966 61860 y Fv(k)g(;\270)39344 61661 y Fq(u)40084 61860 y Fv(k)40654 61661 y Fq(;)221 b(u)41976 61860 y Fv(k)42545 61661 y Fp(i)43062 61883 y Fv(L)43702 61631 y Fe(2)44163 61883 y Fz(\()p Fj(T)45119 61631 y Ff(\244)45599 61883 y Fz(\))46020 61661 y Fq(:)44165 64865 y Fr(\(3.23\))25253 70015 y(15)p eop end %%Page: 16 16 TeXDict begin 16 15 bop 4317 7306 a Fr(When)442 b Fq(A)p Fr(\(0\))g(is)h(negativ)-36 b(e-de\257nite,)442 b(there)g(exists)h Fq(C)479 b(<)383 b Fr(0)443 b(and)f Fq(\270)36768 7505 y Fz(0)37677 7306 y Fq(>)384 b Fr(0)443 b(suc)-36 b(h)441 b(that)h(for)4317 8911 y(an)-36 b(y)434 b Fq(\270)369 b Fp(2)f Fr([0)p Fq(;)221 b(\270)11508 9110 y Fz(0)12035 8911 y Fr(],)434 b(w)-36 b(e)434 b(ha)-36 b(v)g(e)22220 10516 y Fq(A)p Fr(\()p Fq(\270)p Fr(\))369 b Fp(\267)g Fq(C)95 b(I)28337 10715 y Fv(m)29224 10516 y Fq(:)4317 12841 y Fr(As)434 b(the)f(random)g(v)-72 b(ariables)434 b(\()p 19144 12109 858 54 v Fq(!)20002 13040 y Fv(\260)20594 12841 y Fr(\))21100 13097 y Fv(\260)52 b Fk(2)p Fj(Z)22854 12844 y Fi(d)23825 12841 y Fr(are)434 b(negativ)-36 b(e,)435 b(w)-36 b(e)434 b(get)g(that)5424 16435 y Fq(C)7352 15173 y Fl(X)6671 18002 y Fz(1)p Fk(\267)p Fv(k)24 b Fk(\267)p Fv(m)10332 15173 y Fl(X)10173 18100 y Fv(\260)52 b Fk(2)p Fj(Z)11927 17848 y Fi(d)p 12631 15703 V 12631 16435 a Fq(!)13488 16634 y Fv(\260)14081 16435 y Fp(j)p Fr(\()329 b(^)-979 b Fq(u)15696 16634 y Fv(k)16265 16435 y Fr(\)\()p Fq(\260)72 b Fr(\))p Fp(j)18899 15886 y Fz(2)12833 20656 y Fp(\267)15453 19394 y Fl(X)14235 22229 y Fz(1)p Fk(\267)p Fv(k)24 b(;k)16726 21977 y Ff(0)17024 22229 y Fk(\267)p 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Fk(\242)p Fv(\265)28154 65424 y Fq(u)p Fr(\()p Fq(\265)36 b Fr(\))p Fq(d\265)g(:)25253 70015 y Fr(16)p eop end %%Page: 17 17 TeXDict begin 17 16 bop 4317 7306 a Fr(F)-108 b(or)433 b(an)-36 b(y)434 b(\()p Fq(x;)221 b(\265)36 b Fr(\))370 b Fp(2)e Fm(R)14662 6824 y Fv(d)15497 7306 y Fp(\243)296 b Fm(T)17712 6824 y Fk(\244)18671 7306 y Fr(and)433 b(1)369 b Fp(\267)g Fq(k)414 b Fp(\267)369 b Fq(m)p Fr(,)434 b(w)-36 b(e)434 b(set)19171 11122 y Fq(g)19794 11321 y Fv(k)20363 11122 y Fr(\()p Fq(x;)221 b(\265)36 b Fr(\))370 b(=)25221 10223 y Fq(e)25824 9741 y Fv(i)p Fz(\()p Fv(\265)26 b Fk(\241)p Fv(\265)28146 9897 y Fi(k)28654 9741 y Fz(\))p Fk(\242)p Fv(x)30162 10223 y Fp(\241)295 b Fr(1)p 25221 10816 6920 54 v 26216 11082 a Fl(p)p 27544 11082 3602 54 v 1116 x Fq(\263)28112 12397 y Fv(k)24 b(;\270)29492 12198 y Fr(\()p Fq(\265)36 b Fr(\))32273 11122 y Fq(:)11531 b Fr(\(3.25\))4317 15058 y(As)390 b Fq(\265)6801 15257 y Fv(k)7370 15058 y Fr(\()p Fq(\270)p Fr(\))e(is)i(the)f(only)h(zero)g (of)g 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Fq(V)42281 22729 y Fc(e)-570 b Fv(!)42906 22530 y Fp(T)43629 22729 y Fv(')44242 22885 y Fi(k)44806 22530 y Fr(\()p Fq(u)p Fr(\))p Fq(;)221 b Fp(T)47863 22729 y Fv(')48476 22984 y Fi(k)48929 22793 y Ff(0)49339 22530 y Fr(\()p Fq(v)48 b Fr(\))p Fp(i)51545 22786 y Fv(L)52185 22534 y Fe(2)52645 22786 y Fz(\()p Fj(R)53651 22534 y Fi(d)54133 22786 y Fz(\))54554 22530 y Fr(,)4317 24135 y(w)-36 b(e)434 b(get)5424 27973 y Fp(h)p Fq(V)6746 28172 y Fc(e)-570 b Fv(!)7371 27973 y Fp(T)8094 28172 y Fv(')8707 28328 y Fi(k)9271 27973 y Fr(\()p Fq(u)p Fr(\))p Fq(;)221 b Fp(T)12328 28172 y Fv(')12941 28427 y Fi(k)13394 28236 y Ff(0)13804 27973 y Fr(\()p Fq(v)48 b Fr(\))p Fp(i)16010 28229 y Fv(L)16650 27977 y Fe(2)17110 28229 y Fz(\()p Fj(R)18116 27977 y Fi(d)18598 28229 y Fz(\))19314 27973 y Fp(\241)20801 26711 y Fl(X)20642 29638 y Fv(\260)k Fk(2)p Fj(Z)22396 29386 y Fi(d)23160 27973 y Fl(e)-798 b Fq(!)23910 28172 y Fv(\260)24502 26498 y Fl(\263)25517 26165 y(Z)26255 29172 y Fv(C)26926 29295 y Fe(0)27664 27973 y Fq(a)28347 28172 y Fv(';k)24 b(;k)30510 27920 y Ff(0)30863 27973 y Fr(\()p Fq(x)p Fr(\))p Fq(dx)34029 26498 y Fl(\264)35117 27973 y Fp(\242)295 b(j)p Fq(u)p Fr(\()p Fq(\260)72 b Fr(\))p Fp(j)39018 27424 y Fz(2)10069 32194 y Fr(=)11608 30932 y Fl(X)11449 33859 y Fv(\260)52 b Fk(2)p Fj(Z)13203 33607 y Fi(d)13967 32194 y Fl(e)-798 b Fq(!)14717 32393 y Fv(\260)15531 30386 y Fl(Z)16269 33393 y Fv(C)16940 33516 y Fe(0)17677 32194 y Fq(a)18360 32393 y Fv(';k)24 b(;k)20523 32141 y Ff(0)20877 32194 y Fr(\()p Fq(x)p Fr(\))295 b Fp(\242)23587 30720 y Fl(\263)24601 30386 y(Z)25339 33393 y Fj(T)25929 33141 y Ff(\244)26686 32194 y Fq(e)27289 31646 y Fv(i\260)52 b Fk(\242)p Fv(\265)28928 32194 y Fq(g)29551 32393 y Fv(k)30120 32194 y Fr(\()p Fq(x;)221 b(\265)36 b Fr(\))33095 30615 y Fl(q)p 34424 30615 3602 54 v 34424 32194 a Fq(\263)34992 32393 y Fv(k)24 b(;\270)36371 32194 y Fr(\()p Fq(\265)36 b Fr(\))p Fq(u)p Fr(\()p Fq(\265)g Fr(\))p Fq(d\265)g Fp(\242)p 15964 34714 17669 54 v 15964 34873 a Fl(Z)16702 37880 y Fj(T)17292 37628 y Ff(\244)18049 36681 y Fq(e)18652 36297 y Fv(i\260)52 b Fk(\242)p Fv(\265)20291 36681 y Fq(g)20914 36880 y Fv(k)21428 36628 y Ff(0)21781 36681 y Fr(\()p Fq(x;)221 b(\265)36 b Fr(\))24756 35102 y Fl(q)p 26085 35102 3900 54 v 26085 36681 a Fq(\263)26653 36880 y Fv(k)27167 36628 y Ff(0)27465 36880 y Fv(;\270)28331 36681 y Fr(\()p Fq(\265)g Fr(\))o Fq(v)48 b Fr(\()p Fq(\265)36 b Fr(\))p Fq(d\265)33633 35206 y Fl(\264)34426 36681 y Fq(dx)8537 40397 y Fr(+)10003 39135 y Fl(X)9844 42062 y Fv(\260)52 b Fk(2)p Fj(Z)11598 41810 y Fi(d)12362 40397 y Fl(e)-798 b Fq(!)13112 40596 y Fv(\260)13785 40397 y Fr(^)-731 b Fq(u)p Fr(\()p Fq(\260)72 b Fr(\))16424 38589 y Fl(Z)17162 41596 y Fv(C)17833 41719 y Fe(0)18571 40397 y Fq(a)19254 40596 y Fv(';k)24 b(;k)21417 40344 y Ff(0)21770 40397 y Fr(\()p Fq(x)p Fr(\))295 b Fp(\242)p 24480 38429 17669 54 v 24480 38589 a Fl(Z)25218 41596 y Fj(T)25808 41344 y Ff(\244)26565 40397 y Fq(e)27168 40013 y Fv(i\260)52 b Fk(\242)p Fv(\265)28807 40397 y Fq(g)29430 40596 y Fv(k)29944 40344 y Ff(0)30297 40397 y Fr(\()p Fq(x;)221 b(\265)36 b Fr(\))33272 38817 y Fl(q)p 34601 38817 3900 54 v 34601 40397 a Fq(\263)35169 40596 y Fv(k)35683 40344 y Ff(0)35981 40596 y Fv(;\270)36846 40397 y Fr(\()p Fq(\265)g Fr(\))p Fq(v)48 b Fr(\()p Fq(\265)36 b Fr(\))p Fq(d\265)g(dx)8266 44618 y Fr(+)9732 43356 y Fl(X)9573 46283 y Fv(\260)52 b Fk(2)p Fj(Z)11327 46031 y Fi(d)12091 44618 y Fl(e)-798 b Fq(!)12841 44817 y Fv(\260)p 13433 43462 2436 54 v 13482 44618 a Fr(^)-699 b Fq(v)48 b Fr(\()p Fq(\260)72 b Fr(\))16090 42810 y Fl(Z)16828 45817 y Fv(C)17499 45940 y Fe(0)18236 44618 y Fq(a)18919 44817 y Fv(';k)24 b(;k)21082 44565 y Ff(0)21436 44618 y Fr(\()p Fq(x)p Fr(\))295 b Fp(\242)24146 42810 y Fl(Z)24884 45817 y Fj(T)25474 45565 y Ff(\244)26230 44618 y Fq(e)26833 44069 y Fv(i\260)52 b Fk(\242)p Fv(\265)28472 44618 y Fq(g)29095 44817 y Fv(k)29664 44618 y Fr(\()p Fq(x;)221 b(\265)36 b Fr(\))32639 43038 y Fl(q)p 33968 43038 3602 54 v 33968 44618 a Fq(\263)34536 44817 y Fv(k)24 b(;\270)35915 44618 y Fr(\()p Fq(\265)36 b Fr(\))p Fq(u)p Fr(\()p Fq(\265)g Fr(\))p Fq(d\265)g(dx:)1108 b Fr(\(3.27\))4317 49024 y(No)-36 b(w)544 b(using)e(the)h(fact)g(that)g(the)f(family)j(\()60 b Fl(e)-798 b Fq(!)26602 49223 y Fv(\260)27194 49024 y Fr(\))27700 49279 y Fv(\260)52 b Fk(2)p Fj(Z)29454 49027 y Fi(d)30535 49024 y Fr(is)543 b(b)36 b(ounded,)542 b(Cauc)-36 b(h)g(y-Sc)g(h)g(w)g(artz)4317 50629 y(inequalit)g(y)378 b(and)f(P)-36 b(ersev)-72 b(al)378 b(iden)-36 b(tit)g(y)376 b(and)h(equation)h(\(3.26\),)g(w)-36 b(e)377 b(get)h(that)e(there)h (exists)4317 52234 y Fq(C)464 b(>)369 b Fr(0)434 b(suc)-36 b(h)432 b(that)5804 54586 y Fl(X)5645 57514 y Fv(\260)52 b Fk(2)p Fj(Z)7399 57262 y Fi(d)8163 55848 y Fl(e)-797 b Fq(!)8914 56047 y Fv(\260)9727 54040 y Fl(Z)10465 57048 y Fv(C)11136 57171 y Fe(0)11874 55848 y Fq(a)12557 56047 y Fv(';k)24 b(;k)14720 55796 y Ff(0)15073 55848 y Fr(\()p Fq(x)p Fr(\))295 b Fp(\242)17783 54374 y 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