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Author: Camil Muscalu
Publisher: Cambridge University Press
Published: 2013-01-31
Total Pages: 341
ISBN-13: 1107031826
DOWNLOAD EBOOKThis contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author: Camil Muscalu
Publisher: Cambridge University Press
Published: 2013-01-31
Total Pages: 389
ISBN-13: 0521882451
DOWNLOAD EBOOKThis contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author: Yitzhak Katznelson
Publisher:
Published: 1968
Total Pages: 292
ISBN-13:
DOWNLOAD EBOOKAuthor: Ciprian Demeter
Publisher: Cambridge University Press
Published: 2020-01-02
Total Pages: 349
ISBN-13: 1108499708
DOWNLOAD EBOOKComprehensive coverage of recent, exciting developments in Fourier restriction theory, including applications to number theory and PDEs.
Author: Camil Muscalu
Publisher: Cambridge University Press
Published: 2013-01-31
Total Pages: 389
ISBN-13: 1139619160
DOWNLOAD EBOOKThis two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.
Author: Gerlind Plonka
Publisher: Springer
Published: 2019-02-05
Total Pages: 624
ISBN-13: 3030043061
DOWNLOAD EBOOKThis book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.
Author: Gerald B. Folland
Publisher: CRC Press
Published: 2016-02-03
Total Pages: 317
ISBN-13: 1498727158
DOWNLOAD EBOOKA Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
Author: Camil Muscalu
Publisher: Cambridge University Press
Published: 2013-01-31
Total Pages: 341
ISBN-13: 1139620460
DOWNLOAD EBOOKThis two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.
Author: Adrian Constantin
Publisher: Cambridge University Press
Published: 2016-06-02
Total Pages: 368
ISBN-13: 1107044103
DOWNLOAD EBOOKA two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.
Author: Christopher D. Sogge
Publisher: Cambridge University Press
Published: 2017-04-27
Total Pages: 349
ISBN-13: 1107120071
DOWNLOAD EBOOKThis advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.
