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| Softcover ISBN: | 978-1-4704-7062-3 |
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| Softcover ISBN: | 978-1-4704-7062-3 |
| Product Code: | GSM/138.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| Sale Price: | $57.85 |
| eBook ISBN: | 978-0-8218-8995-4 |
| Product Code: | GSM/138.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Sale Price: | $55.25 |
| Softcover ISBN: | 978-1-4704-7062-3 |
| eBook ISBN: | 978-0-8218-8995-4 |
| Product Code: | GSM/138.S.B |
| List Price: | $174.00 $131.50 |
| MAA Member Price: | $156.60 $118.35 |
| AMS Member Price: | $139.20 $105.20 |
| Sale Price: | $113.10 $85.48 |
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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 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.
ReadershipGraduate students and research mathematicians interested in semiclassical and microlocal methods in partial differential equations.
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Table of Contents
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Chapters
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Chapter 1. Introduction
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Part 1. Basic theory
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Chapter 2. Symplectic geometry and analysis
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Chapter 3. Fourier transform, stationary phase
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Chapter 4. Semiclassical quantization
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Part 2. Applications to partial differential equations
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Chapter 5. Semiclassical defect measures
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Chapter 6. Eigenvalues and eigenfunctions
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Chapter 7. Estimates for solutions of PDE
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Part 3. Advanced theory and applications
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Chapter 8. More on the symbol calculus
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Chapter 9. Changing variables
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Chapter 10. Fourier integral operators
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Chapter 11. Quantum and classical dynamics
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Chapter 12. Normal forms
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Chapter 13. The FBI transform
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Part 4. Semiclassical analysis on manifolds
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Chapter 14. Manifolds
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Chapter 15. Quantum ergodicity
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Appendices
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Appendix A. Notation
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Appendix B. Differential forms
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Appendix C. Functional analysis
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Appendix D. Fredholm theory
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Additional Material
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Reviews
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...an excellent and self-contained introduction to the semiclassical and microlocal methods in the study of PDEs.
Zentralblatt MATH
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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
