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View File Name : La-lytv.ps

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dup 0 /.notdef put
readonly def
/FontBBox{-5 -232 545 699}readonly def
/UniqueID 5000830 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX8
%!PS-AdobeFont-1.1: CMBX8 1.0
%%CreationDate: 1991 Aug 20 16:36:07
% 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 (CMBX8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-59 -250 1235 750}readonly def
/UniqueID 5000766 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% 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 (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 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 22 /harpoonupright put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
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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 0 /.notdef put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% 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 (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
/UniqueID 5000788 def
currentdict end
currentfile eexec
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D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4
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cleartomark
%%EndFont 
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% 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 (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{37 -250 1349 750}readonly def
/UniqueID 5087380 def
currentdict end
currentfile eexec
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4C2A259D2A0A1E200F8101469C10D7D537B0D4D39296A9AB3F132DA9A3B459B0
F850E2B3A03BDCB35AEF82285D19C38F474FB414F8EC971B994D1C7DD753B271
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2BFED8236E07820C5BAB411EAE1B31D93A2FA7C374B1725FEC359ABCB88E2C89
214529A263D795AACB0B95A3AB2F4E08EF350C282CE521716DBB06E5B8291B3F
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D64FFF54772B50BB9B173AE79702981F58F9F235C591F476A31852174DF0619C
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0E54AC35106253EE140449425A8670E1F92B178A02A58EB57540F4BD8110E548
BB584EA6D625C5F5FE0124A98E49915F1A1B95D2125874360EED1C4379FEF3C6
90E5780C20309F11F2F23FAD635C44BA030B39EFF083A3ECCDD2641DCB59CC30
728C0DC15829632716892C6A528D0D0B9DD30993C2FDA03E1F150369DF7A5940
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1F40A6C261FDBCC21DEDB39A2974442F40212A220038B86045305FEEF5869774
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EDAA1D72CFD72573F815CF7D242F2F2D5F09E3F86F7FD01AFFC4E7E01C5EDE65
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C3BA6E6CB93DC60F7CDDD085C435F84EA8B3144B4635DE67724A776B914ECEE6
475AC3D9B6DB8A686FC612BA5634B04D51DB725AB3A0FB9605DD4E7BEAC5483E
634A1EDF32172812F6309010D5EC4D2C22C0009E32538F170FEF309679BB2DEB
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A80B1D71D6A85105CE8405E2D93EA79EA25170CA1EB62ED9185EAD7EA448BF2C
80D4A30AA2F15268AAFA864A56EA038F0D23EFF351DE5C86AE4DA0CDA32CA74E
FEEDB5330C2522405C6FDBFFD74A2B04D732F21D942612CC494F86B1B57004A4
7A0728C1E9A7B5EDC7F7B5D93208D8CD47961DED52C485758F2B5C51727C8D87
4D71681E61AD12BE14D2DC9B298335B1C0311F844E38E64BFDA3C7E6FD8D6BC2
6E94C62280C0D2D3CB17A30511620C987F5071FBC5C613E1CD169CA855F37543
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cleartomark
%%EndFont 
%%BeginFont: EUFM7
%!PS-AdobeFont-1.1: EUFM7 2.1
%%CreationDate: 1992 Nov 20 17:36:25
% Euler fonts were designed by Hermann Zapf.
% 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 (EUFM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EUFM7 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 70 /F put
readonly def
/FontBBox{0 -250 1193 750}readonly def
/UniqueID 5031992 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
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cleartomark
%%EndFont 
%%BeginFont: EUFM10
%!PS-AdobeFont-1.1: EUFM10 2.1
%%CreationDate: 1992 Nov 20 17:36:20
% Euler fonts were designed by Hermann Zapf.
% 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 (EUFM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EUFM10 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 70 /F put
readonly def
/FontBBox{-26 -224 1055 741}readonly def
/UniqueID 5031986 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% 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 (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% 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 (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{21 -944 1448 791}readonly def
/UniqueID 5000815 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 82 /R 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: 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 0 /parenleftbig put
dup 1 /parenrightbig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 20 /bracketleftbigg put
dup 21 /bracketrightbigg put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 66 /parenleftex put
dup 67 /parenrightex put
dup 77 /circleplusdisplay put
dup 80 /summationtext put
dup 81 /producttext put
dup 88 /summationdisplay put
dup 89 /productdisplay put
dup 90 /integraldisplay put
dup 122 /bracehtipdownleft put
dup 123 /bracehtipdownright put
dup 124 /bracehtipupleft put
dup 125 /bracehtipupright put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
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%%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 90 /Z put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
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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 0 /.notdef 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 0 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% 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 (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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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 0 /.notdef put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% 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 (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueID 5000772 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%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 0 /.notdef put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 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 0 /.notdef put
readonly def
/FontBBox{-35 -250 1190 750}readonly def
/UniqueID 5000826 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 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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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 0 /.notdef put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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b(REPRESENT)-5 b(A)g(TION)28 b(OF)h(THE)g(JA)n(COBI)h(FIELD)e(OF)h(A)g
(L)2505 35 y(\023)2499 50 y(EVY)g(PR)n(OCESS)176 b(3)0
249 y Fs(Let)27 b Fo(j)p Fq(\013)p Fo(j)p Fs(:=)349 187
y Fl(P)437 207 y Fp(1)437 274 y Fi(i)p Fn(=1)562 249
y Fq(\013)615 261 y Fi(i)643 249 y Fs(.)37 b(F)-7 b(or)26
b(eac)n(h)g Fq(\013)e Fo(2)f Fm(Z)1247 219 y Fp(1)1247
270 y Fn(+)p Fi(;)11 b Fn(0)1367 249 y Fs(,)27 b(1)p
Fq(\013)1512 261 y Fn(1)1566 249 y Fs(+)17 b(2)p Fq(\013)1743
261 y Fn(2)1797 249 y Fs(+)f Fo(\001)e(\001)g(\001)23
b Fs(=)g Fq(n)p Fs(,)k Fq(n)c Fo(2)g Fm(N)p Fs(,)k(and)g(for)f(an)n(y)h
(function)0 363 y Fq(f)41 375 y Fi(n)109 363 y Fs(:)c
Fq(X)231 333 y Fi(n)299 363 y Fo(!)g Fm(R)k Fs(w)n(e)h(de\014ne)f(a)h
(function)g Fq(D)1318 375 y Fi(\013)1365 363 y Fq(f)1406
375 y Fi(n)1474 363 y Fs(:)23 b Fq(X)1596 333 y Fp(j)p
Fi(\013)p Fp(j)1705 363 y Fo(!)g Fm(R)28 b Fs(b)n(y)f(setting)72
504 y(\()p Fq(D)173 516 y Fi(\013)220 504 y Fq(f)261
516 y Fi(n)306 504 y Fs(\)\()p Fq(x)417 516 y Fn(1)455
504 y Fq(;)14 b(:)g(:)g(:)g(;)g(x)687 519 y Fp(j)p Fi(\013)p
Fp(j)774 504 y Fs(\):=)p Fq(f)9 b Fs(\()p Fq(x)1023 516
y Fn(1)1060 504 y Fq(;)14 b(:)g(:)g(:)g(;)g(x)1292 516
y Fi(\013)1335 524 y Fe(1)1372 504 y Fq(;)g(x)1456 516
y Fi(\013)1499 524 y Fe(1)1532 516 y Fn(+1)1620 504 y
Fq(;)g(x)1704 516 y Fi(\013)1747 524 y Fe(1)1780 516
y Fn(+1)1409 559 y Fl(|)p 1446 559 155 10 v 155 w({z)p
1675 559 V 155 w(})1522 637 y Fn(2)23 b(times)1868 504
y Fq(;)14 b(x)1952 516 y Fi(\013)1995 524 y Fe(1)2028
516 y Fn(+2)2116 504 y Fq(;)g(x)2200 516 y Fi(\013)2243
524 y Fe(1)2276 516 y Fn(+2)1905 559 y Fl(|)p 1942 559
V 155 w({z)p 2171 559 V 155 w(})2018 637 y Fn(2)23 b(times)2364
504 y Fq(;)14 b(:)g(:)g(:)g(;)g(x)2596 516 y Fi(\013)2639
524 y Fe(1)2672 516 y Fn(+)p Fi(\013)2766 524 y Fe(2)2803
504 y Fq(;)g(x)2887 516 y Fi(\013)2930 524 y Fe(1)2963
516 y Fn(+)p Fi(\013)3057 524 y Fe(2)2549 559 y Fl(|)p
2586 559 198 10 v 198 w({z)p 2858 559 V 198 w(})2705
637 y Fn(2)22 b(times)3093 504 y Fq(;)991 741 y(x)1038
753 y Fi(\013)1081 761 y Fe(1)1114 753 y Fn(+)p Fi(\013)1208
761 y Fe(2)1240 753 y Fn(+1)1328 741 y Fq(;)14 b(x)1412
753 y Fi(\013)1455 761 y Fe(1)1488 753 y Fn(+)p Fi(\013)1582
761 y Fe(2)1615 753 y Fn(+1)1703 741 y Fq(;)g(x)1787
753 y Fi(\013)1830 761 y Fe(1)1863 753 y Fn(+)p Fi(\013)1957
761 y Fe(2)1989 753 y Fn(+1)991 797 y Fl(|)p 1028 797
469 10 v 469 w({z)p 1571 797 V 469 w(})1418 874 y Fn(3)22
b(times)2078 741 y Fq(;)14 b(:)g(:)g(:)f Fs(\))p Fq(:)100
994 y Fs(W)-7 b(e)28 b(ha)n(v)n(e)e(\(cf.)i([15)o(]\):)0
1158 y Fw(Theorem)j(1.)41 b Fd(F)-6 b(or)30 b(any)g Fq(f)885
1128 y Fn(\()p Fi(n)p Fn(\))982 1158 y Fq(;)14 b(g)1062
1128 y Fn(\()p Fi(n)p Fn(\))1182 1158 y Fo(2)23 b(D)1336
1117 y Fn(^)1326 1128 y Fp(\012)p Fi(n)1423 1158 y Fs(,)30
b Fd(we)g(have)p Fs(:)401 1337 y(\()p Fq(f)483 1303 y
Fn(\()p Fi(n)p Fn(\))580 1337 y Fq(;)14 b(g)660 1303
y Fn(\()p Fi(n)p Fn(\))757 1337 y Fs(\))789 1349 y Fg(F)831
1357 y Ff(n)899 1337 y Fs(=)1292 1258 y Fl(X)986 1436
y Fi(\013)p Fp(2)p Fk(Z)1113 1416 y Fj(1)1113 1455 y
Fe(+)p Ff(;)c Fe(0)1217 1436 y Fn(:)h(1)p Fi(\013)1323
1444 y Fe(1)1356 1436 y Fn(+2)p Fi(\013)1483 1444 y Fe(2)1516
1436 y Fn(+)p Fp(\001\001\001)o Fn(=)p Fi(n)1732 1337
y Fq(K)1803 1349 y Fi(\013)1863 1224 y Fl(Z)1909 1413
y Fi(X)1968 1396 y Fj(j)p Ff(\013)p Fj(j)2053 1337 y
Fs(\()p Fq(D)2154 1349 y Fi(\013)2201 1337 y Fq(f)2242
1349 y Fi(n)2287 1337 y Fs(\)\()p Fq(x)2398 1349 y Fn(1)2436
1337 y Fq(;)j(:)g(:)g(:)g(;)g(x)2668 1352 y Fp(j)p Fi(\013)p
Fp(j)2755 1337 y Fs(\))979 1583 y Fo(\002)k Fs(\()p Fq(D)1163
1595 y Fi(\013)1210 1583 y Fq(g)1250 1595 y Fi(n)1295
1583 y Fs(\)\()p Fq(x)1406 1595 y Fn(1)1444 1583 y Fq(;)c(:)g(:)g(:)g
(;)g(x)1676 1598 y Fp(j)p Fi(\013)p Fp(j)1763 1583 y
Fs(\))g Fq(\033)1859 1549 y Fp(\012j)p Fi(\013)p Fp(j)1998
1583 y Fs(\()p Fq(dx)2120 1595 y Fn(1)2158 1583 y Fq(;)g(:)g(:)g(:)g(;)
g(dx)2433 1598 y Fp(j)p Fi(\013)p Fp(j)2520 1583 y Fs(\))p
Fq(;)0 1724 y Fd(wher)l(e)0 1913 y Fs(\(6\))668 b Fq(K)845
1925 y Fi(\013)915 1913 y Fs(=)1013 1857 y(\(1)p Fq(\013)1140
1869 y Fn(1)1195 1857 y Fs(+)18 b(2)p Fq(\013)1373 1869
y Fn(2)1428 1857 y Fs(+)h Fo(\001)14 b(\001)g(\001)f
Fs(\)!)p 1013 1894 666 4 v 1169 1970 a Fq(\013)1222 1982
y Fn(1)1260 1970 y Fs(!)h Fq(\013)1350 1982 y Fn(2)1387
1970 y Fs(!)g Fo(\001)g(\001)g(\001)1723 1834 y Fl(Y)1715
2013 y Fi(k)q Fp(\025)p Fn(2)1851 1796 y Fl(\022)1922
1793 y(Q)2000 1814 y Fi(k)q Fp(\000)p Fn(1)2000 1880
y Fi(i)p Fn(=1)2140 1855 y Fq(b)2176 1867 y Fi(i)p 1922
1894 282 4 v 2028 1970 a Fq(k)s Fs(!)2213 1796 y Fl(\023)2274
1813 y Fn(2)p Fi(\013)2350 1822 y Ff(k)2391 1913 y Fq(:)100
2175 y Fs(Next,)25 b(w)n(e)f(\014nd)h(the)g(elemen)n(ts)g(whic)n(h)f(b)
r(elong)g(to)h(the)f(space)g Fh(F)2086 2187 y Fi(n)2156
2175 y Fs(after)g(the)h(completion)f(of)h Fo(D)3078 2134
y Fn(^)3068 2145 y Fp(\012)p Fi(n)3165 2175 y Fs(.)0
2274 y(T)-7 b(o)27 b(this)h(end,)g(w)n(e)f(de\014ne,)h(for)f(eac)n(h)g
Fq(\013)c Fo(2)h Fm(Z)1373 2244 y Fp(1)1373 2295 y Fn(+)p
Fi(;)11 b Fn(0)1493 2274 y Fs(,)27 b(the)h(Hilb)r(ert)g(space)649
2441 y Fq(L)706 2407 y Fn(2)706 2462 y Fi(\013)753 2441
y Fs(\()p Fq(X)861 2407 y Fp(j)p Fi(\013)p Fp(j)947 2441
y Fq(;)14 b(\033)1034 2407 y Fp(\012j)p Fi(\013)p Fp(j)1173
2441 y Fs(\):=)p Fq(L)1350 2407 y Fn(2)1387 2441 y Fs(\()p
Fq(X)r(;)g(\033)s Fs(\))1618 2396 y Fn(^)1609 2407 y
Fp(\012)p Fi(\013)1704 2415 y Fe(1)1759 2441 y Fo(\012)k
Fq(L)1899 2407 y Fn(2)1936 2441 y Fs(\()p Fq(X)r(;)c(\033)s
Fs(\))2167 2396 y Fn(^)2158 2407 y Fp(\012)p Fi(\013)2253
2415 y Fe(2)2309 2441 y Fo(\012)k(\001)c(\001)g(\001)27
b Fq(:)0 2582 y Fs(De\014ne)h(a)f(mapping)622 2735 y
Fq(U)688 2701 y Fn(\()p Fi(n)p Fn(\))808 2735 y Fs(:)c
Fo(D)930 2690 y Fn(^)920 2701 y Fp(\012)p Fi(n)1040 2735
y Fo(!)1450 2656 y Fl(M)1147 2834 y Fi(\013)p Fp(2)p
Fk(Z)1274 2814 y Fj(1)1274 2853 y Fe(+)p Ff(;)9 b Fe(0)1377
2834 y Fn(:)j(1)p Fi(\013)1484 2842 y Fe(1)1516 2834
y Fn(+2)p Fi(\013)1643 2842 y Fe(2)1676 2834 y Fn(+)p
Fp(\001\001\001)o Fn(=)p Fi(n)1892 2735 y Fq(L)1949 2701
y Fn(2)1949 2755 y Fi(\013)1996 2735 y Fs(\()p Fq(X)2104
2701 y Fp(j)p Fi(\013)p Fp(j)2190 2735 y Fq(;)i(\033)2277
2701 y Fp(\012j)p Fi(\013)p Fp(j)2416 2735 y Fs(\))p
Fq(K)2519 2747 y Fi(\013)0 3001 y Fs(b)n(y)37 b(setting,)i(for)d(eac)n
(h)g Fq(f)814 2970 y Fn(\()p Fi(n)p Fn(\))950 3001 y
Fo(2)j(D)1120 2960 y Fn(^)1110 2971 y Fp(\012)1162 2970
y Fi(n)1207 3001 y Fs(,)h(the)d Fq(L)1479 2970 y Fn(2)1479
3021 y Fi(\013)1526 3001 y Fs(\()p Fq(X)1634 2970 y Fp(j)p
Fi(\013)p Fp(j)1720 3001 y Fq(;)14 b(\033)1807 2970 y
Fp(\012j)p Fi(\013)p Fp(j)1946 3001 y Fs(\))p Fq(K)2049
3013 y Fi(\013)2096 3001 y Fs(-co)r(ordinate)36 b(of)g
Fq(U)2711 2970 y Fn(\()p Fi(n)p Fn(\))2808 3001 y Fq(f)2858
2970 y Fn(\()p Fi(n)p Fn(\))2992 3001 y Fs(to)h(b)r(e)0
3103 y Fq(D)69 3115 y Fi(\013)116 3103 y Fq(f)166 3073
y Fn(\()p Fi(n)p Fn(\))263 3103 y Fs(.)49 b(By)31 b(virtue)h(of)f
(Theorem)g(1,)i Fq(U)1333 3073 y Fn(\()p Fi(n)p Fn(\))1461
3103 y Fs(ma)n(y)e(b)r(e)h(extended)g(b)n(y)g(con)n(tin)n(uit)n(y)f(to)
g(an)h(isometric)0 3203 y(mapping)27 b(of)h Fh(F)487
3215 y Fi(n)559 3203 y Fs(in)n(to)1176 3242 y Fl(M)873
3420 y Fi(\013)p Fp(2)p Fk(Z)1000 3400 y Fj(1)1000 3439
y Fe(+)p Ff(;)9 b Fe(0)1104 3420 y Fn(:)i(1)p Fi(\013)1210
3428 y Fe(1)1242 3420 y Fn(+2)p Fi(\013)1369 3428 y Fe(2)1402
3420 y Fn(+)p Fp(\001\001\001)o Fn(=)p Fi(n)1618 3321
y Fq(L)1675 3287 y Fn(2)1675 3341 y Fi(\013)1722 3321
y Fs(\()p Fq(X)1830 3287 y Fp(j)p Fi(\013)p Fp(j)1916
3321 y Fq(;)j(\033)2003 3287 y Fp(\012j)p Fi(\013)p Fp(j)2142
3321 y Fs(\))p Fq(K)2245 3333 y Fi(\013)2292 3321 y Fq(:)0
3550 y Fs(F)-7 b(urthermore,)27 b(w)n(e)g(ha)n(v)n(e)f(\(cf.)j([9)o(,)f
(15)o(]\):)0 3703 y Fw(Theorem)j(2.)41 b Fd(The)31 b(mapping)656
3856 y Fq(U)722 3821 y Fn(\()p Fi(n)p Fn(\))842 3856
y Fs(:)23 b Fh(F)939 3868 y Fi(n)1007 3856 y Fo(!)1416
3777 y Fl(M)1113 3955 y Fi(\013)p Fp(2)p Fk(Z)1240 3935
y Fj(1)1240 3974 y Fe(+)p Ff(;)9 b Fe(0)1344 3955 y Fn(:)i(1)p
Fi(\013)1450 3963 y Fe(1)1483 3955 y Fn(+2)p Fi(\013)1610
3963 y Fe(2)1642 3955 y Fn(+)p Fp(\001\001\001)o Fn(=)p
Fi(n)1858 3856 y Fq(L)1915 3821 y Fn(2)1915 3876 y Fi(\013)1962
3856 y Fs(\()p Fq(X)2070 3821 y Fp(j)p Fi(\013)p Fp(j)2156
3856 y Fq(;)j(\033)2243 3821 y Fp(\012j)p Fi(\013)p Fp(j)2382
3856 y Fs(\))p Fq(K)2485 3868 y Fi(\013)0 4094 y Fd(is)30
b(a)g(unitary)g(op)l(ertator)p Fs(.)100 4247 y(By)d(virtue)g(of)h
(Theorem)f(2)g(and)g(\(5\),)h(w)n(e)f(can)g(iden)n(tify)i
Fh(F)1933 4259 y Fi(n)2005 4247 y Fs(with)f(the)g(space)1187
4326 y Fl(M)884 4504 y Fi(\013)p Fp(2)p Fk(Z)1011 4484
y Fj(1)1011 4523 y Fe(+)p Ff(;)10 b Fe(0)1115 4504 y
Fn(:)h(1)p Fi(\013)1221 4512 y Fe(1)1254 4504 y Fn(+2)p
Fi(\013)1381 4512 y Fe(2)1414 4504 y Fn(+)p Fp(\001\001\001)o
Fn(=)p Fi(n)1630 4405 y Fq(L)1687 4371 y Fn(2)1687 4425
y Fi(\013)1733 4405 y Fs(\()p Fq(X)1841 4371 y Fp(j)p
Fi(\013)p Fp(j)1928 4405 y Fq(;)j(\033)2015 4371 y Fp(\012j)p
Fi(\013)p Fp(j)2154 4405 y Fs(\))p Fq(K)2257 4417 y Fi(\013)0
4647 y Fs(and)27 b(the)h(space)f Fh(F)h Fs(with)836 4721
y Fl(M)784 4899 y Fi(\013)p Fp(2)p Fk(Z)911 4879 y Fj(1)911
4918 y Fe(+)p Ff(;)9 b Fe(0)1028 4799 y Fq(L)1085 4765
y Fn(2)1085 4820 y Fi(\013)1132 4799 y Fs(\()p Fq(X)1240
4765 y Fp(j)p Fi(\013)p Fp(j)1326 4799 y Fq(;)14 b(\033)1413
4765 y Fp(\012j)p Fi(\013)p Fp(j)1552 4799 y Fs(\))p
Fq(K)1655 4811 y Fi(\013)1703 4799 y Fs(\(1)p Fq(\013)1830
4811 y Fn(1)1885 4799 y Fs(+)k(2)p Fq(\013)2063 4811
y Fn(2)2118 4799 y Fs(+)h Fo(\001)14 b(\001)g(\001)f
Fs(\)!)h Fq(:)0 5041 y Fs(F)-7 b(or)27 b(a)g(v)n(ector)f
Fq(f)32 b Fo(2)24 b Fh(F)p Fs(,)j(w)n(e)g(will)h(denote)g(its)f
Fq(\013)p Fs(-co)r(ordinate)g(b)n(y)g Fq(f)2028 5053
y Fi(\013)2103 5041 y Fs(.)100 5141 y(Note)g(that,)h(for)f(for)g
Fq(\013)d Fs(=)e(\()p Fq(n;)14 b Fs(0)p Fq(;)g Fs(0)p
Fq(;)g(:)g(:)g(:)f Fs(\),)28 b(w)n(e)f(ha)n(v)n(e)363
5297 y Fq(L)420 5263 y Fn(2)420 5317 y Fi(\013)467 5297
y Fs(\()p Fq(X)575 5263 y Fp(j)p Fi(\013)p Fp(j)661 5297
y Fq(;)14 b(\033)748 5263 y Fp(\012j)p Fi(\013)p Fp(j)887
5297 y Fs(\))23 b(=)g Fq(L)1087 5263 y Fn(2)1124 5297
y Fs(\()p Fq(X)r(;)14 b(\033)s Fs(\))1355 5252 y Fn(^)1346
5263 y Fp(\012)p Fi(n)1444 5297 y Fq(;)96 b(K)1634 5309
y Fi(\013)1704 5297 y Fs(=)23 b(1)p Fq(;)96 b Fs(\(1)p
Fq(\013)2080 5309 y Fn(1)2136 5297 y Fs(+)18 b(2)p Fq(\013)2314
5309 y Fn(2)2369 5297 y Fs(+)g Fo(\001)c(\001)g(\001)g
Fs(\)!)23 b(=)g Fq(n)p Fs(!)p Fq(:)p eop end
%%Page: 4 4
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b(YTVYNO)n(V)0 249 y Fs(Hence,)28 b(the)g(space)f Fh(F)g
Fs(con)n(tains)g(the)h(symmetric)f(F)-7 b(o)r(c)n(k)27
b(space)1001 453 y Fo(F)8 b Fs(\()p Fq(L)1158 418 y Fn(2)1195
453 y Fs(\()p Fq(X)r(;)14 b(\033)s Fs(\)\))24 b(=)1591
349 y Fp(1)1561 374 y Fl(M)1561 550 y Fi(n)p Fn(=0)1700
453 y Fq(L)1757 418 y Fn(2)1794 453 y Fs(\()p Fq(X)r(;)14
b(\033)s Fs(\))2025 407 y Fn(^)2016 418 y Fp(\012)p Fi(n)2114
453 y Fq(n)p Fs(!)0 666 y(as)30 b(a)g(prop)r(er)f(subspace.)45
b(Therefore,)30 b(w)n(e)g(call)g Fh(F)g Fs(an)g(extended)h(F)-7
b(o)r(c)n(k)30 b(space.)44 b(W)-7 b(e)31 b(also)f(note)g(that)0
766 y(the)e(space)f Fh(F)g Fs(satis\014es)g(the)h(axioms)f(of)g(an)g
(in)n(teracting)g(F)-7 b(o)r(c)n(k)27 b(space,)g(see)g([11)o(].)100
865 y(In)k(the)g(space)g Fq(L)636 835 y Fn(2)672 865
y Fs(\()p Fo(D)770 835 y Fp(0)794 865 y Fq(;)14 b(\026)p
Fs(\),)32 b(w)n(e)f(consider,)g(for)g(eac)n(h)f Fq(')f
Fo(2)g(D)r Fs(,)j(the)g(op)r(erator)d Fq(M)9 b Fs(\()p
Fq(')p Fs(\))32 b(of)f(m)n(ultipli-)0 965 y(cation)e(b)n(y)f(the)i
(function)g Fo(h\001)p Fq(;)14 b(')p Fo(i)p Fs(.)42 b(Let)30
b Fq(J)8 b Fs(\()p Fq(')p Fs(\))26 b(:=)f Fo(U)8 b Fq(M)h
Fs(\()p Fq(')p Fs(\))p Fo(U)1872 935 y Fp(\000)p Fn(1)1962
965 y Fs(.)42 b(Denote)29 b(b)n(y)g Fo(F)2490 977 y Fn(\014n)2568
965 y Fs(\()p Fo(D)r Fs(\))i(the)e(set)g(of)g(all)0 1075
y(v)n(ectors)g(of)i(the)h(form)e(\()p Fq(f)802 1087 y
Fn(0)840 1075 y Fq(;)14 b(f)918 1087 y Fn(1)954 1075
y Fq(;)g(:)g(:)g(:)g(;)g(f)1180 1087 y Fi(n)1225 1075
y Fq(;)g Fs(0)p Fq(;)g Fs(0)p Fq(;)g(:)g(:)g(:)e Fs(\),)32
b Fq(f)1657 1087 y Fi(i)1713 1075 y Fo(2)d(D)1873 1034
y Fn(^)1863 1045 y Fp(\012)q Fi(i)1943 1075 y Fs(,)j
Fq(i)c Fs(=)h(0)p Fq(;)14 b(:)g(:)g(:)f(;)h(n)p Fs(,)31
b Fq(n)e Fo(2)g Fm(Z)2697 1087 y Fn(+)2752 1075 y Fs(.)48
b(Eviden)n(tly)-7 b(,)0 1175 y Fo(F)60 1187 y Fn(\014n)138
1175 y Fs(\()p Fo(D)r Fs(\))29 b(is)e(a)g(dense)h(subset)f(of)h
Fh(F)p Fs(.)37 b(W)-7 b(e)28 b(ha)n(v)n(e)e(the)i(follo)n(wing)f
(theorem,)g(see)g([8].)0 1328 y Fw(Theorem)k(3.)41 b
Fd(F)-6 b(or)30 b(any)g Fq(')24 b Fo(2)f(D)r Fs(,)30
b Fd(we)g(have)p Fs(:)0 1470 y(\(7\))268 b Fo(F)434 1482
y Fn(\014n)512 1470 y Fs(\()p Fo(D)r Fs(\))24 b Fo(\032)f
Fs(Dom\()p Fq(J)8 b Fs(\()p Fq(')p Fs(\)\))p Fq(;)100
b(J)8 b Fs(\()p Fq(')p Fs(\))24 b Fc(\026)f Fo(F)1601
1482 y Fn(\014n)1679 1470 y Fs(\()p Fo(D)r Fs(\))h(=)f
Fq(J)1975 1436 y Fn(+)2030 1470 y Fs(\()p Fq(')p Fs(\))c(+)f
Fq(J)2304 1436 y Fn(0)2341 1470 y Fs(\()p Fq(')p Fs(\))i(+)e
Fq(J)2616 1436 y Fp(\000)2672 1470 y Fs(\()p Fq(')p Fs(\))p
Fq(:)0 1612 y Fd(Her)l(e,)30 b Fq(J)278 1582 y Fn(+)333
1612 y Fs(\()p Fq(')p Fs(\))h Fd(is)f(the)g(usual)f(cr)l(e)l(ation)h
(op)l(er)l(ator)p Fs(:)0 1768 y(\(8\))734 b Fq(J)894
1734 y Fn(+)949 1768 y Fs(\()p Fq(')p Fs(\))p Fq(f)1108
1780 y Fi(n)1177 1768 y Fs(=)22 b Fq(')1330 1755 y Fs(^)1318
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b(The)34 b(family)g(of)0 4311 y(op)r(erators)26 b(\()p
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%%Page: 5 5
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249 y Fs(Consider)27 b(the)h(tensor)e(pro)r(duct)i Fq(`)1086
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b(o)r(c)n(k)27 b(space)g(o)n(v)n(er)f Fq(`)1574 773 y
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1053 y Fq(`)498 1065 y Fn(2)p Fi(;)p Fn(0)588 1053 y
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1235 y Fs(with)g(domain)f Fq(`)2981 1247 y Fn(2)p Fi(;)p
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1517 y(\(11\))452 b Fq(J)8 b(e)693 1529 y Fi(n)761 1517
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y Fs(+)g Fq(b)1593 1529 y Fi(n)1638 1517 y Fq(e)1677
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b Fq(J)887 1768 y Fn(0)942 1798 y Fs(+)g Fq(J)1079 1768
y Fp(\000)1135 1798 y Fs(.)100 1898 y(Denote)34 b(b)n(y)f(\010)h(the)g
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1910 y Fn(2)1640 1898 y Fo(\012)22 b Fq(L)1784 1868 y
Fn(2)1821 1898 y Fs(\()p Fq(X)r(;)14 b(\033)s Fs(\)\))35
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b(acuum)24 b(v)n(ector)f(\(1)p Fq(;)14 b Fs(0)p Fq(;)g
Fs(0)p Fq(;)g(:)g(:)g(:)e Fs(\))24 b(and)g(v)n(ectors)f(of)h(the)g
(form)g(\()p Fq(\030)15 b Fo(\012)c Fq(')p Fs(\))2088
1967 y Fp(\012)p Fi(n)2186 1998 y Fs(,)25 b(where)e Fq(\030)k
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y Fn(2)1935 2097 y Fo(\012)18 b Fq(L)2075 2067 y Fn(2)2112
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2197 y Fs(,)28 b(w)n(e)f(set)610 2382 y Fq(A)672 2347
y Fn(+)727 2382 y Fs(\()p Fq(')p Fs(\)\()p Fq(\030)d
Fo(\012)18 b Fq( )s Fs(\))1109 2347 y Fp(\012)p Fi(n)1206
2382 y Fs(:=\()p Fq(e)1365 2394 y Fn(0)1420 2382 y Fo(\012)g
Fq(')p Fs(\))1601 2369 y(^)1589 2382 y Fo(\012)q Fs(\()p
Fq(\030)23 b Fo(\012)18 b Fq( )s Fs(\))1918 2347 y Fp(\012)p
Fi(n)0 2382 y Fs(\(12\))1308 2527 y(+)g Fq(n)p Fs(\(\()p
Fq(J)1559 2492 y Fn(+)1614 2527 y Fq(\030)t Fs(\))h Fo(\012)f
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Fs(\()p Fq(\030)23 b Fo(\012)18 b Fq(')p Fs(\))2321 2492
y Fp(\012)p Fn(\()p Fi(n)p Fp(\000)p Fn(1\))2555 2527
y Fq(;)627 2672 y(A)689 2637 y Fn(0)727 2672 y Fs(\()p
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2637 y Fp(\012)p Fi(n)1206 2672 y Fs(:=)p Fq(n)p Fs(\(\()p
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Fs(\()p Fq(\030)23 b Fo(\012)18 b Fq(')p Fs(\))2206 2637
y Fp(\012)p Fn(\()p Fi(n)p Fp(\000)p Fn(1\))2441 2672
y Fq(;)609 2817 y(A)671 2783 y Fp(\000)727 2817 y Fs(\()p
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2783 y Fp(\012)p Fi(n)1206 2817 y Fs(:=)p Fq(n)p Fo(h)p
Fq(\030)t(;)c(e)1492 2829 y Fn(0)1529 2817 y Fo(ih)p
Fq(';)g( )s Fo(i)p Fs(\()p Fq(\030)24 b Fo(\012)18 b
Fq(')p Fs(\))2034 2783 y Fp(\012)p Fn(\()p Fi(n)p Fp(\000)p
Fn(1\))1308 2962 y Fs(+)g Fq(n)p Fs(\(\()p Fq(J)1559
2928 y Fp(\000)1615 2962 y Fq(\030)t Fs(\))h Fo(\012)f
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Fs(\))i(+)e Fq(a)1843 3292 y Fn(0)1880 3326 y Fs(\()p
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1959 y(Res.)d(Inst.)g(Math.)f(Sci.)h Fb(22)f Fv(\(1986\),)i(209{246.)0
2042 y(11.)35 b(Z.)20 b(Huang)h(and)g(Y.)f(W)-6 b(u,)21
b Fu(Inter)l(acting)h(F)-5 b(o)l(ck)23 b(exp)l(ansion)h(of)f(L)n(\023)
-35 b(evy)22 b(white)g(noise)h(functionals)p Fv(,)e(Acta)g(Appl.)f
(Math.)125 2125 y Fb(82)j Fv(\(2004\),)i(333{352.)0 2208
y(12.)35 b(K.)21 b(It^)-35 b(o,)23 b Fu(Sp)l(e)l(ctr)l(al)i(typ)l(e)e
(of)h(the)g(shift)f(tr)l(ansformation)j(of)d(di\013er)l(ential)h(pr)l
(o)l(c)l(esses)i(with)e(stationary)f(incr)l(ements)p
Fv(,)125 2291 y(T)-6 b(rans.)23 b(Amer.)g(Math.)h(So)r(c.)g
Fb(81)f Fv(\(1956\),)i(253{266.)0 2374 y(13.)35 b(Y.)28
b(Kondrtatiev)i(and)f(E.)e(Lytvyno)n(v,)k Fu(Op)l(er)l(ators)g(of)g
(gamma)g(white)f(noise)g(c)l(alculus)p Fv(,)g(In\014n.)f(Dimens.)e
(Anal.)125 2457 y(Quan)n(tum)e(Probab.)f(Relat.)f(T)-6
b(op.)24 b Fb(3)f Fv(\(2000\),)i(303{335.)0 2540 y(14.)35
b(E.)21 b(Lytvyno)n(v,)i Fu(Polynomials)i(of)e(Meixner's)f(typ)l(e)h
(in)g(in\014nite)f(dimensions|Jac)l(obi)j(\014elds)f(and)f(ortho)l
(gonality)125 2623 y(me)l(asur)l(es)p Fv(,)i(J.)f(F)-6
b(unct.)24 b(Anal.)f Fb(200)g Fv(\(2003\),)i(118{149.)0
2707 y(15.)35 b(E.)e(Lytvyno)n(v,)j Fu(Ortho)l(gonal)g(de)l(c)l(omp)l
(ositions)g(for)f(L)n(\023)-35 b(evy)33 b(pr)l(o)l(c)l(esses)j(with)e
(an)h(applic)l(ation)h(to)e(the)g(Gamma,)125 2790 y(Pasc)l(al,)f(and)e
(Meixner)e(pr)l(o)l(c)l(esses)p Fv(,)i(In\014n.)e(Dimens.)f(Anal.)f
(Quan)n(tum)j(Probab.)e(Relat.)h(T)-6 b(op.)28 b Fb(6)g
Fv(\(2003\),)j(73{)125 2873 y(102.)0 2956 y(16.)k(E.)27
b(Lytvyno)n(v,)j Fu(The)g(squar)l(e)g(of)f(white)g(noise)h(as)g(a)f
(Jac)l(obi)h(\014eld)p Fv(,)f(In\014n.)f(Dimens.)f(Anal.)f(Quan)n(tum)j
(Probab.)125 3039 y(Relat.)24 b(T)-6 b(op.)24 b Fb(7)f
Fv(\(2004\),)i(619{629.)0 3122 y(17.)35 b(E.)c(Lytvyno)n(v,)j
Fu(L)n(\023)-35 b(evy)32 b(pr)l(o)l(c)l(esses)i(and)f(Jac)l(obi)g
(\014elds)p Fv(,)g(to)e(app)r(ear)g(in)g(Pro)r(ceedings)g(of)g(the)h(V)
-6 b(olterra{CIRM{)125 3205 y(Greifsw)n(ald)26 b(In)n(ternational)h
(Conference)g(Classical)e(and)i(Quan)n(tum)g(Levy)g(Pro)r(cesses:)36
b(Theory)26 b(and)g(Applica-)125 3288 y(tions,)e(Levico)g(T)-6
b(erme)24 b(\(T)-6 b(ren)n(to,)25 b(Italy\),)f(Septem)n(b)r(er)h
(27-Octob)r(er)g(3,)e(2003.)0 3371 y(18.)35 b(A.)23 b(V.)g(Sk)n(oroho)r
(d,)i Fu(Inte)l(gr)l(ation)h(in)g(Hilb)l(ert)f(Sp)l(ac)l(e)p
Fv(,)f(Springer-V)-6 b(erlag,)23 b(New)h(Y)-6 b(ork,)23
b(1974.)100 3526 y Ft(Dep)l(ar)l(tment)i(of)h(Ma)l(thema)l(tics,)f
(University)i(of)f(W)-8 b(ales)27 b(Sw)-6 b(ansea,)26
b(Singleton)g(P)-6 b(ark,)27 b(Sw)-6 b(ansea)26 b(SA2)0
3609 y(8PP,)g(U.K.)100 3692 y Fu(E-mail)g(addr)l(ess)5
b Fv(:)33 b Fa(e.lytvynov@swansea.ac.uk)p eop end
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