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Semiclassical Analysis

About this Title

Maciej Zworski, University of California, Berkeley, Berkeley, CA

Publication: Graduate Studies in Mathematics
Publication Year: 2012; Volume 138
ISBNs: 978-0-8218-8320-4 (print); 978-0-8218-8995-4 (online)
DOI: https://doi.org/10.1090/gsm/138
MathSciNet review: MR2952218
MSC: Primary 58J40; Secondary 35P05, 35S05, 81Q20

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Table of Contents

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Front/Back Matter

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Chapters

• Chapter 1. Introduction

Part 1. Basic theory

• Chapter 2. Symplectic geometry and analysis
• Chapter 3. Fourier transform, stationary phase
• Chapter 4. Semiclassical quantization

Part 2. Applications to partial differential equations

• Chapter 5. Semiclassical defect measures
• Chapter 6. Eigenvalues and eigenfunctions
• Chapter 7. Estimates for solutions of PDE

Part 3. Advanced theory and applications

• Chapter 8. More on the symbol calculus
• Chapter 9. Changing variables
• Chapter 10. Fourier integral operators
• Chapter 11. Quantum and classical dynamics
• Chapter 12. Normal forms
• Chapter 13. The FBI transform

Part 4. Semiclassical analysis on manifolds

• Chapter 14. Manifolds
• Chapter 15. Quantum ergodicity

Appendices

• Appendix A. Notation
• Appendix B. Differential forms
• Appendix C. Functional analysis
• Appendix D. Fredholm theory