Bopp Pseudo-Differential Operators and Deformation Quantization (Pseudo-Differential Operators) 〈Vol.5〉

Gosson, Maurice A. de

BIRKHÄUSER（2011/03発売）

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製本 Paperback:紙装版/ペーパーバック版／ページ数 400 p.
商品コード 9783764399917

Full Description

The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature.

Foreword.- Preface.- Prologue.- Part I: Symplectic Mechanics.- 1. Hamiltonian Mechanics in a Nutshell.- 2. The Symplectic Group.- 3. Free Symplectic Matrices.- 4. The Group of Hamiltonian Symplectomorphisms.- 5. Symplectic Capacities.- 6. Uncertainty Principles.- Part II: Harmonic Analysis in Symplectic Spaces.- 7. The Metaplectic Group.- 8. Heisenberg-Weyl and Grossmann-Royer Operators.- 9. Cross-ambiguity and Wigner Functions.- 10. The Weyl Correspondence.- 11. Coherent States and Anti-Wick Quantization.- 12. Hilbert-Schmidt and Trace Class Operators.- 13. Density Operator and Quantum States.- Part III: Pseudo-differential Operators and Function Spaces.- 14. Shubin's Global Operator Calculus.- Part IV: Applications.- 15. The Schrodinger Equation.- 16. The Feichtinger Algebra.- 17. The Modulation Spaces Mqs.- 18. Bopp Pseudo-differential Operators.- 19. Applications of Bopp Quantization.- Bibliography.- Index.