相空間中的調和分析（簡體書）

《相空間中的調和分析》內容簡介：The phrase harmonic analysis in phase space is a concise if somewhatinadequate name for the area of analysis on Rn that involves the Heisenberggroup, quantization, the Weyl operational calculus, the metaplectic representa-tion, wave packets, and related concepts: it is meant to suggest analysis on theconfiguration space Rn done by working in the phase space Rn x Rn. The ideasthat fall under this rubric have originated in several different fidds――Fourieranalysis, partial differential equations, mathematical physics, representationtheory, and number theory, among others.本書是相空間中調和分析方面的一本專著。主要介紹了Heisenberg群表示定理，擬微分算子的Weyl運算，Weyl運算框架下的波包變換，及Metaplectic表示，並收錄了該領域近年來的一些研究成果。本書內容豐富，行文流暢，相信此書的出版將會給致力於此專業的學者提供極大幫助。讀者對象為數學專業的研究生和教學工作者。主要目次：Heisenberg群及其表示；量化和擬微分算子；波包和波前；Metaplectic表示；振盪半群。

Preface
Prologue. Some Matters of Notation
CHAPTER 1.
THE HEISENBERG GROUP AND ITS REPRESENTATIONS
1. Background from physics
Hamiltonian mechanics, 10. Quantum mechanics, 12. Quantization, 15.
2. The Heisenberg group
The automorphisms of the Heisenberg group, 19.
3. The SchrSdinger representation
The integrated representation, 23. Twisted convolution, 25.
The uncertainty principle, 27.
4. The Fourier-Wigner transform
Radar ambiguity functions, 33.
5. The Stone-von Neumann theorem
The group Fourier transform, 37.
6. The Fock-Bargmann representation
Some motivation and history, 47.
7. Hermite functions
8. The Wigner transform
9. The Laguerre connection
10. The nilmanifold representation
11. Postscripts

CHAPTER 2.
QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS
1. The Weyl correspondence
Covariance properties, 83. Symbol classes, 86. Miscellaneous remarks
and examples, 90.
2. The Kohn-Nirenberg correspondence
3. The product formula
4. Basic pseudodifferential theory
Wave front sets, 118.
5. The CalderSn-Vaillancourt theorems
6. The sharp Garding inequality
7. The Wick and anti-Wick correspondences

CHAPTER 3.
WAVE PACKETS AND WAVE FRONTS
1. Wave packet expansions
2. A characterization of wave front sets
3. Analyticity and the FBI transform
4. Gabor expansions

CHAPPTER 4.
THE METAPLECTIC REPRESENTATION
1. Symplectic linear algebra
2. Construction of the metaplectic representation
The Fock model, 180.
3. The infinitesimal representation
4. Other aspects of the metaplectic representation
Integral formulas, 191. Irreducible subspaces, 194. Dependence on
Plancks constant, 195. The extended metaplectic representation, 196.
The Groenewold-van Hove theorems, 197. Some applications, 199.
5. Gaussians and the symmetric space
Characterizations of Gaussians, 206.
6. The disc model
7. Variants and analogues
Restrictions of the metaplectic representation, 216. U(n,n) as a complex
symplectic group, 217. The spin representation, 220.

CHAPTER 5.
THE OSCILLATOR SEMIGROUP
1. The SchrSdinger model
The extended oscillator semigroup, 234.
2. The Hermite semigroup
3. Normalization and the Cayley transform
4. The Fock model
Appendix A. Gaussian Integrals and a Lemma on Determinants
Appendix B. Some Hilbert Space Results
Bibliography
Index