相空间中的调和分析

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作　者：	（美）福兰地著
出版社：	世界图书出版公司
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标　签：	数学分析

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ISBN：	9787510005428	出版时间：	2009-08-01	包装：	平装
开本：	24开	页数：	277	字数：

内容简介

　　Thephrase"harmonicanalysisinphasespace"isaconciseifsomewhatinadequatenamefortheareaofanalysisonRnthatinvolvestheHeisenberggroup，quantization，theWeyloperationalcalculus，themetaplecticrepresentation，wavepackets，andrelatedconcepts：itismeanttosuggestanalysisontheconfigurationspaceRndonebyworkinginthephasespaceRn×Rn.Theideasthatfallunderthisrubrichaveoriginatedinseveraldifferentfields：Fourieranalysis，partialdifferentialequations，mathematicalphysics，representationtheory，andnumbertheory，amongothers.Asaresult，althoughtheseideasareindividuallywellknowntoworkersinsuchfields，theirclosekinshipandthecross-fertilizationtheycanprovidehaveoftenbeeninsufficientlyappreciated.Oneoftheprincipalobjectivesofthismonographistogiveacoherentaccountofthismaterial，comprisingnotjustanefficienttourofthemajoravenuesbutalsoanexplorationofsomepicturesquebyways.

作者简介

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图书目录

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