Classical and Multilinear Harmonic Analysis: Volume 1
Classical and Multilinear Harmonic Analysis: Volume 1

Author: Camil Muscalu

Publisher: Cambridge University Press

Published: 2013-01-31

Total Pages: 389

ISBN-13: 1139619160

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This 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.

Classical and Multilinear Harmonic Analysis
Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu

Publisher:

Published: 2013

Total Pages:

ISBN-13: 9781139047081

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"This 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"--

Classical and Multilinear Harmonic Analysis
Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu

Publisher: Cambridge University Press

Published: 2013-01-31

Total Pages: 341

ISBN-13: 1107031826

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This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Classical and Multilinear Harmonic Analysis: Volume 2
Classical and Multilinear Harmonic Analysis: Volume 2

Author: Camil Muscalu

Publisher: Cambridge University Press

Published: 2013-01-31

Total Pages: 341

ISBN-13: 1139620460

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This 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.

Classical and Multilinear Harmonic Analysis
Classical and Multilinear Harmonic Analysis

Author: Camil Muscallu

Publisher:

Published: 2013

Total Pages: 324

ISBN-13: 9781107237889

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"This 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"--

Classical and Multilinear Harmonic Analysis
Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu

Publisher:

Published: 2014-05-14

Total Pages: 390

ISBN-13: 9781139624749

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This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Classical and Multilinear Harmonic Analysis
Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu

Publisher: Cambridge University Press

Published: 2013-01-31

Total Pages: 389

ISBN-13: 0521882451

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This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Numerical Fourier Analysis
Numerical Fourier Analysis

Author: Gerlind Plonka

Publisher: Springer

Published: 2019-02-05

Total Pages: 624

ISBN-13: 3030043061

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This 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.