Semiclassical Analysis

Häftad, Engelska, 2012

Del i serien Graduate Studies in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2012-05-30
Mått:250 x 20 x 170 mm
Vikt:795 g
Format:Häftad
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:431
Förlag:American Mathematical Society
ISBN:9781470470623

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Maciej Zworski, University of California, Berkeley, CA.

Recensioner i media

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

Innehållsförteckning

IntroductionBasic theory: Symplectic geometry and analysisFourier transform, stationary phaseSemiclassical quantizationApplications to partial differential equations: Semiclassical defect measuresEigenvalues and eigenfunctionsEstimates for solutions of PDEAdvanced theory and applications: More on the symbol calculusChanging variablesFourier integral operatorsQuantum and classical dynamicsNormal formsThe FBI transformSemiclassical analysis on manifolds: ManifoldsQuantum ergodicityAppendices: NotationDifferential formsFunctional analysisFredholm theoryBibliographyIndex