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Time-frequency analysis of operators. (English) Zbl 07204958

De Gruyter Studies in Mathematics 75. Berlin: De Gruyter (ISBN 978-3-11-053035-3/hbk; 978-3-11-053245-6/ebook). xiv, 442 p. (2020).
Preliminary review / Publisher’s 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

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
35S05 Pseudodifferential operators as generalizations of partial differential operators
42Bxx Harmonic analysis in several variables
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