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Semiclassical Analysis

Maciej Zworski University of California, Berkeley, Berkeley, CA
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Softcover ISBN: 978-1-4704-7062-3
Product Code: GSM/138.S
List Price: $80.00 MAA Member Price:$72.00
AMS Member Price: $64.00 Electronic ISBN: 978-0-8218-8995-4 Product Code: GSM/138.E List Price:$75.00
MAA Member Price: $67.50 AMS Member Price:$60.00
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List Price: $120.00 MAA Member Price:$108.00
AMS Member Price: $96.00 Click above image for expanded view Semiclassical Analysis Maciej Zworski University of California, Berkeley, Berkeley, CA Available Formats:  Softcover ISBN: 978-1-4704-7062-3 Product Code: GSM/138.S  List Price:$80.00 MAA Member Price: $72.00 AMS Member Price:$64.00
 Electronic ISBN: 978-0-8218-8995-4 Product Code: GSM/138.E
 List Price: $75.00 MAA Member Price:$67.50 AMS Member Price: $60.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$120.00 MAA Member Price: $108.00 AMS Member Price:$96.00
• Book Details

Volume: 1382012; 431 pp
MSC: 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 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.

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

• Reviews

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

Zentralblatt MATH
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1382012; 431 pp
MSC: 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 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.

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

Zentralblatt MATH
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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