相空間中的調和分析簡(jiǎn)介，目錄書(shū)摘
2020-02-11 14:28
來(lái)源：京東
作者：京東
相空間中的調和分析
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編輯推薦: The main point of Chapter 2 is the development of the Weyl calculusof pseudodifferential operators.
內容簡(jiǎn)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.
目錄: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
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
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