Semiclassical analysis
著者
書誌事項
Semiclassical analysis
（Graduate studies in mathematics, 138）（Applied mathematics）
American Mathematical Society, 2022, c2012
- : softcover
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注記
Includes bibliographical references (p. 421-426) and index
内容説明・目次
内容説明
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.
目次
Introduction
Basic theory: Symplectic geometry and analysis
Fourier transform, stationary phase
Semiclassical quantization
Applications to partial differential equations: Semiclassical defect measures
Eigenvalues and eigenfunctions
Estimates for solutions of PDE
Advanced theory and applications: More on the symbol calculus
Changing variables
Fourier integral operators
Quantum and classical dynamics
Normal forms
The FBI transform
Semiclassical analysis on manifolds: Manifolds
Quantum ergodicity
Appendices: Notation
Differential forms
Functional analysis
Fredholm theory
Bibliography
Index
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