Harmonic Analysis in Phase Space
eBook - PDF

Harmonic Analysis in Phase Space

  1. 288 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Harmonic Analysis in Phase Space

About this book

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.

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Yes, you can access Harmonic Analysis in Phase Space by Gerald B. Folland in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. CONTENTS
  5. PREFACE
  6. Prologue. Some Matters of Notation
  7. CHAPTER 1. THE HEISENBERG GROUP AND ITS REPRESENTATIONS
  8. CHAPTER 2. QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS
  9. CHAPTER 3. WAVE PACKETS AND WAVE FRONTS
  10. CHAPTER 4. THE METAPLECTIC REPRESENTATION
  11. CHAPTER 5. THE OSCILLATOR SEMIGROUP
  12. Appendix A. Gaussian Integrals and a Lemma on Determinants
  13. Appendix B. Some Hilbert Space Results
  14. Bibliography
  15. Index