Harmonic Analysis in Phase Space. (AM-122), Volume 122 / Gerald B. Folland.

Format:

Book

Author/Creator:

Folland, Gerald B., author.

Series:

Annals of mathematics studies ; no. 122.

Annals of Mathematics Studies ; 353

Language:

English

Subjects (All):

Phase space (Statistical physics).

Harmonic analysis.

Physical Description:

1 online resource (289 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

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.

Contents:

Frontmatter

CONTENTS

PREFACE

PROLOGUE. SOME MATTERS OF NOTATION

CHAPTER 1. THE HEISENBERG GROUP AND ITS REPRESENTATIONS

CHAPTER 2. QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS

CHAPTER 3. WAVE PACKETS AND WAVE FRONTS

CHAPTER 4. THE METAPLECTIC REPRESENTATION

CHAPTER 5. THE OSCILLATOR SEMIGROUP

APPENDIX A. GAUSSIAN INTEGRALS AND A LEMMA ON DETERMINANTS

APPENDIX B. SOME HILBERT SPACE RESULTS

BIBLIOGRAPHY

INDEX

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882427

1400882427

OCLC:

979633761