Del 0 - Graduate Studies in Mathematics

Semiclassical Analysis

Häftad, Engelska, 2012

1 399 kr

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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

Utgivningsdatum2012-05-30
Mått250 x 20 x 170 mm
Vikt795 g
FormatHäftad
SpråkEngelska
SerieGraduate Studies in Mathematics
Antal sidor431
FörlagAmerican Mathematical Society
ISBN9781470470623

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Beräkning och matematisk analys inom Naturvetenskap och teknik

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