Semiclassical Analysis

Maciej Zworski, University of California, Berkeley, CA.

• 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

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