E-Book, Englisch, 288 Seiten
Folland Harmonic Analysis in Phase Space
1. Auflage 2016
ISBN: 978-1-4008-8242-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 288 Seiten
Reihe: Annals of Mathematics Studies
ISBN: 978-1-4008-8242-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Autoren/Hrsg.
Weitere Infos & Material
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
