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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[This book] is a valiant attempt to present an account of [harmonic analysis in phase space], with an emphasis on the analysis-quantum mechanics and pseudodifferential operators.... The author has taken great pains to express himself clearly and ... the notation is consistent throughout.... The author should be congratulated on a very valuable addition to the library of harmonic analysis. -- Zentralblatt für Mathematik
--This text refers to the Paperback edition.
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First Sentence:
The Heisenberg group and its Lie algebra were born long before they were christened. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oscillator semigroup, metaplectic representation, wave packet transform, twisted convolution, conic neighborhood, imprimitivity theorem, infinitesimal automorphisms, wave front set, pseudodifferential operators, twisted product, symplectic form, intertwining operators, quantum observables, ambiguity functions, irreducible unitary representations, analytic vectors, spin representation, symplectic group Key Phrases - Capitalized Phrases (CAPs): (learn more)
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The Heisenberg group and its Lie algebra were born long before they were christened. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oscillator semigroup, metaplectic representation, wave packet transform, twisted convolution, conic neighborhood, imprimitivity theorem, infinitesimal automorphisms, wave front set, pseudodifferential operators, twisted product, symplectic form, intertwining operators, quantum observables, ambiguity functions, irreducible unitary representations, analytic vectors, spin representation, symplectic group Key Phrases - Capitalized Phrases (CAPs): (learn more)
Stone-von Neumann New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 27
books:
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65
books
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- Harmonic Analysis by Elias M. Stein in Back Matter (1), and Back Matter (2)
- Special Functions: Group Theoretical Aspects and Applications (Mathematics and Its Applications) by R.A. Askey in Back Matter
- Hardy Spaces on Homogeneous Groups. (MN-28): (Mathematical Notes) by Gerald B. Folland in Back Matter
- Mathematical Problems of Relativistic Physics (Lectures in Applied Mathematics Series, Vol 2) by E. E. Segal in Back Matter
- Symplectic Techniques in Physics by Victor Guillemin in Back Matter
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- Wavelets, Volume 2: A Tutorial in Theory and Applications (Wavelet Analysis and Its Applications) by Charles K. Chui on page 395, page 537, and Back Matter
- Advances in Gabor Analysis by Hans G. Feichtinger on page 126, page 150, and page 193
- Time Frequency Analysis by Boualme Boashash on page 127, page 144, and Back Matter
- Wavelet Transforms & Time-Frequency Signal Analysis by Lokenath Debnath on page 289, and page 321
- Pseudo-Differential Operators and Related Topics (Operator Theory: Advances and Applications) by Paolo Boggiatto on page 225, and Back Matter
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