Overview

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.

Full Product Details

Author:   M.W. Wong
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1998
Dimensions:   Width: 15.50cm , Height: 0.90cm , Length: 23.50cm
Weight:   0.272kg
ISBN:  

9781475771749

ISBN 10:   1475771746
Pages:   160
Publication Date:   08 March 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

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.

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