Harmonic Analysis in Phase Space

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Princeton University Press, 1989 - Mathematics - 277 pages
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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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Contents

Prologue Some Matters of Notation
3
CHAPTER
9
CHAPTER 2
76
WAVE PACKETS AND WAVE FRONTS
143
CHAPTER 4
168
CHAPTER 5
223
Appendix A Gaussian Integrals and a Lemma on Determinants
256
Bibliography
265
Index
275
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About the author (1989)

Gerald B. Folland was born and raised in Salt Lake City, Utah. He received his bachelor's degree from Harvard University in 1968 and his doctorate from Princeton University in 1971. After two years at the Courant Institute, he moved to the University of Washington, where he is now professor of mathematics. He is the author of ten textbooks and research monographs in the areas of real analysis, harmonic analysis, partial differential equations, and mathematical physics.

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