Harmonic Analysis in Phase Space. (AM-122)

Harmonic Analysis in Phase Space. (AM-122)

ISBN-10:
0691085285
ISBN-13:
9780691085289
Pub. Date:
03/01/1989
Publisher:
Princeton University Press

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Overview

Harmonic Analysis in Phase Space. (AM-122)

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Product Details

ISBN-13: 9780691085289
Publisher: Princeton University Press
Publication date: 03/01/1989
Series: Annals of Mathematics Studies Series , #12
Edition description: New Edition
Pages: 288
Product dimensions: 6.00(w) x 9.00(h) x 0.80(d)

Table of Contents

  • Frontmatter, pg. i
  • CONTENTS, pg. v
  • PREFACE, pg. vii
  • PROLOGUE. SOME MATTERS OF NOTATION, pg. 1
  • CHAPTER 1. THE HEISENBERG GROUP AND ITS REPRESENTATIONS, pg. 9
  • CHAPTER 2. QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS, pg. 78
  • CHAPTER 3. WAVE PACKETS AND WAVE FRONTS, pg. 143
  • CHAPTER 4. THE METAPLECTIC REPRESENTATION, pg. 170
  • CHAPTER 5. THE OSCILLATOR SEMIGROUP, pg. 223
  • APPENDIX A. GAUSSIAN INTEGRALS AND A LEMMA ON DETERMINANTS, pg. 256
  • APPENDIX B. SOME HILBERT SPACE RESULTS, pg. 260
  • BIBLIOGRAPHY, pg. 265
  • INDEX, pg. 275

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