Time-Frequency Analysis of Operators

Elena Cordero; Luigi Rodino

Published by De Gruyter 2020

Time-Frequency Analysis of Operators

Elena Cordero and Luigi Rodino

Volume 75 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110532456

Overview
Contents

About this book

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

Author / Editor information

Elena Cordero and Luigi Rodino, University of Turin, Italy.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Introduction Publicly Available Download PDF	IX
Contents Publicly Available Download PDF	XI
0 Preliminaries Requires Authentication Unlicensed Licensed Download PDF	1
1 Basics of time–frequency representations and related properties Requires Authentication Unlicensed Licensed Download PDF	9
2 Function spaces Requires Authentication Unlicensed Licensed Download PDF	69
3 Gabor frames and linear operators Requires Authentication Unlicensed Licensed Download PDF	143
4 Pseudodifferential operators Requires Authentication Unlicensed Licensed Download PDF	191
5 Time–frequency analysis of constant-coefficient partial differential equations Requires Authentication Unlicensed Licensed Download PDF	277
6 Fourier integral operators and applications to Schrödinger equations Requires Authentication Unlicensed Licensed Download PDF	325
A Appendix Requires Authentication Unlicensed Licensed Download PDF	409
Bibliography Requires Authentication Unlicensed Licensed Download PDF	425
Index Requires Authentication Unlicensed Licensed Download PDF	439
Index of Notation Requires Authentication Unlicensed Licensed Download PDF	441

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in mathematical analysis.
Pages
- Front matter: 14
- Main content: 444
Illustrations
- Illustrations: 27
Keywords: Fourier-Integraloperator; Gabor-Transformation; Nichtlineare Wellengleichung; Pseudodifferentialoperator; Zeit-Frequenz-Analyse

eBook

Published: September 21, 2020
ISBN: 9783110532456

Hardcover

Published: September 21, 2020
ISBN: 9783110530353