on the theory of generalized hilbert transforms …on the theory of generalized hilbert transforms...

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Research Report KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017) On the theory of generalized Hilbert transforms Chapter V The spectre analysis and synthesis on the N.Wiener class S by Sumiyuki Koizumi Sumiyuki Koizumi Department of Mathematics Faculty of Science and Technology Keio University Department of Mathematics Faculty of Science and Technology Keio University c 2017 KSTS 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 Japan

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Page 1: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

Research Report

KSTS/RR-16/004November 25, 2016

(Second edition, August 24, 2017)

On the theory of generalized Hilbert transformsChapter V

The spectre analysis and synthesis on the N.Wiener class S

by

Sumiyuki Koizumi

Sumiyuki KoizumiDepartment of MathematicsFaculty of Science and TechnologyKeio University

Department of MathematicsFaculty of Science and TechnologyKeio University

c©2017 KSTS3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 Japan

Page 2: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 3: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 4: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 5: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 6: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 7: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 8: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 9: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 10: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 11: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 12: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 13: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 14: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 15: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 16: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 17: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

KSTS/RR-16/004 November 25, 2016 (Second edition, August 24, 2017)

Page 18: On the theory of generalized Hilbert transforms …On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysis and synthesis on the N.Wiener class S (2)), KSTS/RR-17/005,

Department of MathematicsFaculty of Science and Technology

Keio University

Research Report

2016

[16/001]　　

Shiro Ishikawa,Linguistic interpretation of quantum mechanics: Quantum Language [Ver. 2 ],KSTS/RR-16/001, January 8, 2016

[16/002]　　

Yuka Hashimoto, Takashi Nodera,Inexact shift-invert Arnoldi method for evolution equations,KSTS/RR-16/002, May 6, 2016

[16/003]　　

Yuka Hashimoto, Takashi Nodera,A Note on Inexact Rational Krylov Method for Evolution Equations,KSTS/RR-16/003, November 9, 2016

[16/004]　　

Sumiyuki Koizumi,On the theory of generalized Hilbert transforms (Chapter V: The spectre analysisand synthesis on the N.Wiener class S ),KSTS/RR-16/004, November 25, 2016 (Second edition, August 24, 2017)

[16/005]　　

Shiro Ishikawa,History of Western Philosophy from the quantum theoretical point of view,KSTS/RR-16/005, December 6, 2016

2017

[17/001]　　

Yuka Hashimoto, Takashi Nodera,Inexact Shift-invert Rational Krylov Method for Evolution Equations,KSTS/RR-17/001, January 27, 2017 (Revised July 24, 2017)

[17/002]　　

Dai Togashi, Takashi Nodera,Convergence analysis of the GKB-GCV algorithm,KSTS/RR-17/002, March 27, 2017

[17/003]　　

Shiro Ishikawa,Linguistic solution to the mind-body problem,KSTS/RR-17/003, April 3, 2017

[17/004]　　

Shiro Ishikawa,History of Western Philosophy from the quantum theoretical point of view; Version 2,KSTS/RR-17/004, May 12, 2017

[17/005]　　　

Sumiyuki Koizumi,On the theory of generalized Hilbert transforms (Chapter VI: The spectre analysisand synthesis on the N.Wiener class S (2)),KSTS/RR-17/005, June 8, 2017 (Second edition, September 1, 2017)

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