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Book DetailsGraduate Studies in MathematicsVolume: 138; 2012; 431 ppMSC: Primary 35; 81;
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 classicalquantum (particlewave) correspondence. These techniques include such wellknown 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.ReadershipGraduate students and research mathematicians interested in semiclassical and microlocal methods in partial differential equations.

Table of Contents

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


Additional Material

Reviews

...an excellent and selfcontained introduction to the semiclassical and microlocal methods in the study of PDEs.
Zentralblatt MATH


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 Book Details
 Table of Contents
 Additional Material
 Reviews

 Request Review Copy
 Request Exam/Desk Copy
 Get Permissions
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 classicalquantum (particlewave) correspondence. These techniques include such wellknown 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.
Graduate students and research mathematicians interested in semiclassical and microlocal methods in partial differential equations.

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

...an excellent and selfcontained introduction to the semiclassical and microlocal methods in the study of PDEs.
Zentralblatt MATH