Time-Frequency Analysis of Operators

Description

This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems.　　　　 The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines. A comprehensive text on the time-frequency analysis of operators Provides an overview of the subject by two leading experts in operator theory Stresses the application part, including numerical aspects and nonlinear equations Preface Introduction Contents 0 Preliminaries 1 Basics of time–frequency representations and related properties 2 Function spaces 3 Gabor frames and linear operators 4 Pseudodifferential operators 5 Time–frequency analysis of constant-coefficient partial differential equations 6 Fourier integral operators and applications to Schrödinger equations A Appendix Bibliography Index Index of Notation