M. W. Wong: Weyl Transforms | Taschenbuch

Cover: 9780387984148 | Weyl Transforms | M. W. Wong | Taschenbuch | viii | Englisch | 1998

Rückseite: 9780387984148 | Weyl Transforms | M. W. Wong | Taschenbuch | viii | Englisch | 1998

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Beschreibung

This book is an outgrowth of courses given by me for graduate students at York University in the past ten years. The actual writing of the book in this form was carried out at York University, Peking University, the Academia Sinica in Beijing, the University of California at Irvine, Osaka University, and the University of Delaware. The idea of writing this book was ?rst conceived in the summer of 1989, and the protracted period of gestation was due to my daily duties as a professor at York University. I would like to thank Professor K. C. Chang, of Peking University; Professor Shujie Li, of the Academia Sinica in Beijing; Professor Martin Schechter, of the University of California at Irvine; Professor Michihiro Nagase, of Osaka University; and Professor M. Z. Nashed, of the University of Delaware, for providing me with stimulating environments for the exchange of ideas and the actual writing of the book. We study in this book the properties of pseudo-differential operators arising in quantum mechanics, ?rst envisaged in [33] by Hermann Weyl, as bounded linear 2 n operators on L (R ). Thus, it is natural to call the operators treated in this book Weyl transforms.

Zusammenfassung

This book studies properties of pseudo-differential operators arising in quantum mechanics as bounded linear operators on $ L^ä2ü(BbbR^änü) $. The results and methods should be of interest to graduate students and mathematicians working in Fourier analysis, operator theory, pseudo-differential operators and mathematical physics. Background materials are given in adequate detail to enable a graduate student to proceed rapidly from the very basics to the frontier of resarch in an area of operator theory.

Inhaltsverzeichnis

Prerequisite Topics in Fourier Analysis.- The Fourier-Wigner Transform.- The Wigner Transform.- The Weyl Transform.- Hilbert-Schmidt Operators on L2(?n).- The Tensor Product in L2(?n).- H*-Algebras and the Weyl Calculus.- The Heisenberg Group.- The Twisted Convolution.- The Riesz-Thorin Theorem.- Weyl Transforms with Symbols in Lr(?2n), 1 ? r ? 2.- Weyl Transforms with Symbols in L?(?2n).- Weyl Transforms with Symbols in Lr(?2n), 2 r < ?.- Compact Weyl Transforms.- Localization Operators.- A Fourier Transform.- Compact Localization Operators.- Hermite Polynomials.- Hermite Functions.- Laguerre Polynomials.- Hermite Functions on ?.- Vector Fields on ?.- Laguerre Formulas for Hermite Functions on ?.- Weyl Transforms on L2(?) with Radial Symbols.- Another Fourier Transform.- A Class of Compact Weyl Transforms on L2(?).- A Class of Bounded Weyl Transforms on L2(?).- A Weyl Transform with Symbol in S'(?2).- The Symplectic Group.- Symplectic Invariance of Weyl Transforms.

Erscheinungsjahr:	1998
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	viii 160 S.
ISBN-13:	9780387984148
ISBN-10:	0387984143
Sprache:	Englisch
Herstellernummer:	10663135
Einband:	Kartoniert / Broschiert
Autor:	Wong, M. W.
Hersteller:	Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 10 mm
Von/Mit:	M. W. Wong
Erscheinungsdatum:	21.08.1998
Gewicht:	0,271 kg

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