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Harmonic analysis in phase space /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton Univ Press,
2016.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; CONTENTS; PREFACE; Prologue. Some Matters of Notation ; CHAPTER 1. THE HEISENBERG GROUP AND ITS REPRESENTATIONS ; 1. Background from physics ; Hamiltonian mechanics ; Quantum mechanics ; Quantization ; 2. The Heisenberg group ; The automorphisms of the Heisenberg group.
- 3. The Schrödinger representationThe integrated representation ; Twisted convolution ; The uncertainty principle ; 4. The Fourier-Wigner transform; Radar ambiguity functions ; 5. The St one-von Neumann theorem; The group Fourier transform ; 6. The Fock-Bargmann representation; Some motivation and history ; 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 ; Symbol classes ; Miscellaneous remarks and examples ; 2. The Kohn-Nirenberg correspondence.
- 3. The product formula 4. Basic pseudodifferential theory ; Wave front sets ; 5. The Calderón-Vaillancourt theorems; 6. The sharp Gårding 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 ; CHAPTER 4. THE METAPLECTIC REPRESENTATION ; 1. Symplectic linear algebra ; 2. Construction of the metaplectic representation ; The Fock model ; 3. The infinitesimal representation.