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Classical and multilinear harmonic a...

Muscalu, Camil,

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Classical and multilinear harmonic analysis /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Classical and multilinear harmonic analysis // Camil Muscalu, Wilhelm Schlag.
作者:	Muscalu, Camil,
其他作者:	Schlag, Wilhelm,
出版者:	Cambridge, UK :Cambridge University Press, : 2013.,
面頁冊數:	2 v. :ill. :24 cm.
標題:	Harmonic analysis. -
電子資源:	http://assets.cambridge.org/97805218/82453/cover/9780521882453.jpg
ISBN:	1107032628 (hbk. : set ) :

Classical and multilinear harmonic analysis /
Muscalu, Camil,

Classical and multilinear harmonic analysis /Camil Muscalu, Wilhelm Schlag. - Cambridge, UK :Cambridge University Press,2013. - 2 v. :ill. :24 cm. - Cambridge studies in advanced mathematics ;137-138.

Includes bibliographical references and indexes.

Fourier series : convergence and summability -- v. 1 --

"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"--

ISBN: 1107032628 (hbk. : set ) :US135.00 (2 vol.)

LCCN: 2012024828Subjects--Topical Terms:

555704
Harmonic analysis.

LC Class. No.: QA403 / .M87 2013

Dewey Class. No.: 515/.2422

Classical and multilinear harmonic analysis /
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245 1 0 $a Classical and multilinear harmonic analysis / $c Camil Muscalu, Wilhelm Schlag.
260 # $a Cambridge, UK : $b Cambridge University Press, $c 2013.
300 $a 2 v. : $b ill. : $b ill ; $c 24 cm.
490 1 0 $a Cambridge studies in advanced mathematics ; $v 137-138
504 $a Includes bibliographical references and indexes.
505 0 # $g v. 1 -- $t Fourier series : convergence and summability -- $t Harmonic functions ; Poisson kernel -- $t Conjugate harmonic fuctions ; Hilbert transform -- $t The Fourier transform on R[superscript d] and on LCA groups -- $t Introduction to probability theory -- $t Fourier series and randomness -- $t Calderâon-Zygmund theory of singular integrals -- $t Littlewood-Paley theory -- $t Almost orthogonality -- $t The uncertainty principle -- $t Fourier restriction and applications -- $t Introduction to the Weyl calculus -- $g v. 2 -- $t Leibnitz rules and the generalized Korteweg-de Vries equation -- $t Classical paraproducts -- $t Paraproducts on polydisks -- $t Calderâon commutators and the Cauchy integral on Lipschitz curves -- $t Iterated Fourier series and physical reality -- $t The bilinear Hilbert transform -- $t Almost everywhere convergence of Fourier series -- $t Flag paraproducts -- $t Appendix : multilinear interpolation.
520 # $a "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"-- $c Provided by publisher.
650 # 0 $a Harmonic analysis. $3 555704
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