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Weyl Transforms

  • Textbook
  • © 1998

Overview

Authors:
  1. M. W. Wong

    1. Department of Mathematics and Statistics, York University, Toronto, Canada

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Part of the book series: Universitext (UTX)

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Table of contents (30 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Prerequisite Topics in Fourier Analysis

    Pages 1-8

  3. The Fourier-Wigner Transform

    Pages 9-11

  4. The Wigner Transform

    Pages 13-17

  5. The Weyl Transform

    Pages 19-24

  6. Hilbert-Schmidt Operators on L2(ℝn)

    Pages 25-27

  7. The Tensor Product in L2(ℝn)

    Pages 29-32

  8. H*-Algebras and the Weyl Calculus

    Pages 33-35

  9. The Heisenberg Group

    Pages 37-42

  10. The Twisted Convolution

    Pages 43-46

  11. The Riesz-Thorin Theorem

    Pages 47-53

  12. Weyl Transforms with Symbols in Lr(ℝ2n), 1 ≤ r ≤ 2

    Pages 55-58

  13. Weyl Transforms with Symbols in L∞(ℝ2n)

    Pages 59-62

  14. Weyl Transforms with Symbols in Lr(ℝ2n), 2 < r < ∞

    Pages 63-69

  15. Compact Weyl Transforms

    Pages 71-74

  16. Localization Operators

    Pages 75-78

  17. A Fourier Transform

    Pages 79-81

  18. Compact Localization Operators

    Pages 83-85

  19. Hermite Polynomials

    Pages 87-91

  20. Hermite Functions

    Pages 93-94
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Statistics, York University, Toronto, Canada

    M. W. Wong

Bibliographic Information

  • Book Title: Weyl Transforms

  • Authors: M. W. Wong

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/b98973

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-387-98414-8Published: 21 August 1998

  • Softcover ISBN: 978-1-4757-7174-9Published: 08 March 2013

  • eBook ISBN: 978-0-387-22778-8Published: 31 March 2006

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: VIII, 160

  • Topics: Topological Groups, Lie Groups

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