**Graduate Studies in Mathematics**

Volume: 138;
2012;
431 pp;
Hardcover

MSC: Primary 35; 81;

Print ISBN: 978-0-8218-8320-4

Product Code: GSM/138

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-8995-4
Product Code: GSM/138.E**

List Price: $75.00

Individual Member Price: $60.00

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#### Supplemental Materials

# Semiclassical Analysis

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*Maciej Zworski*

This book is an excellent, comprehensive introduction to semiclassical analysis. I believe it will become a standard reference for the subject.

—Alejandro Uribe, University of Michigan

Semiclassical analysis provides PDE techniques based on the
classical-quantum (particle-wave) correspondence. These
techniques include such well-known tools as geometric optics and the
Wentzel–Kramers–Brillouin approximation. Examples of problems
studied in this subject are high energy eigenvalue asymptotics and
effective dynamics for solutions of evolution equations. From the
mathematical point of view, semiclassical analysis is a branch of
microlocal analysis which, broadly speaking, applies harmonic
analysis and symplectic geometry to the study of linear and
nonlinear PDE. The book is intended to be a graduate level text
introducing readers to semiclassical and microlocal methods in PDE. It
is augmented in later chapters with many specialized advanced topics
which provide a link to current research literature.

#### Table of Contents

# Table of Contents

## Semiclassical Analysis

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface xi12 free
- Chapter 1. Introduction 114 free
- Chapter 2. Symplectic geometry and analysis 1326
- Chapter 3. Fourier transform, stationary phase 2740
- Chapter 4. Semiclassical quantization 5568
- Chapter 5. Semiclassical defect measures 99112
- Chapter 6. Eigenvalues and eigenfunctions 119132
- Chapter 7. Estimates for solutions of PDE 139152
- Chapter 8. More on the symbol calculus 171184
- Chapter 9. Changing variables 197210
- Chapter 10. Fourier integral operators 219232
- Chapter 11. Quantum and classical dynamics 245258
- Chapter 12. Normal forms 273286
- Chapter 13. The FBI transform 291304
- Chapter 14. Manifolds 339352
- Chapter 15. Quantum ergodicity 365378
- Appendix A. Notation 383396
- Appendix B. Differential forms 391404
- Appendix C. Functional analysis 399412
- Appendix D. Fredholm theory 415428
- Bibliography 421434
- Index 427440 free
- Back Cover Back Cover1448

#### Readership

Graduate students and research mathematicians interested in semiclassical and microlocal methods in partial differential equations.

#### Reviews

...an excellent and self-contained introduction to the semiclassical and microlocal methods in the study of PDEs.

-- Zentralblatt MATH