Harmonic Analysis in Phase Space.

by Gerald B. Folland

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.

Genres: Mathematics

288 pages, Paperback

First published January 1, 1989

Reviews

[Ida · Rating 5 out of 5]

If you are looking for similar content, put this book on top of your list. It's well written and engaging. The chapters follow each other logically and there's a comfortable - not slow - pace of progression. It's a joy to read and work through it you want to read it from cover to cover.

[Sarah · Rating 4 out of 5]

Very clear and useful exposition of the representation theory and integral transforms on he Heisenberg group.