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Analysis on h-harmonics and Dunkl transforms

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Analysis on h-harmonics and Dunkl transforms/ by Feng Dai, Yuan Xu ; edited by Sergey Tikhonov.
Author:	Dai, Feng.
other author:	Xu, Yuan.
Published:	Basel :Springer Basel : : 2015.,
Description:	viii, 118 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Harmonic analysis. -
Online resource:	http://dx.doi.org/10.1007/978-3-0348-0887-3
ISBN:	9783034808873 (electronic bk.)

Analysis on h-harmonics and Dunkl transforms
Dai, Feng.

Analysis on h-harmonics and Dunkl transforms[electronic resource] /by Feng Dai, Yuan Xu ; edited by Sergey Tikhonov. - Basel :Springer Basel :2015. - viii, 118 p. :ill., digital ;24 cm. - Advanced courses in mathematics, CRM Barcelona,2297-0304. - Advanced courses in mathematics, CRM Barcelona..

Preface -- Spherical harmonics and Fourier transform -- Dunkl operators associated with reflection groups -- h-Harmonics and analysis on the sphere -- Littlewood–Paley theory and the multiplier theorem -- Sharp Jackson and sharp Marchaud inequalities -- Dunkl transform -- Multiplier theorems for the Dunkl transform -- Bibliography.

As a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a bare minimum.

ISBN: 9783034808873 (electronic bk.)

Standard No.: 10.1007/978-3-0348-0887-3doiSubjects--Topical Terms:

672073
Harmonic analysis.

LC Class. No.: QA403

Dewey Class. No.: 515.2433

Analysis on h-harmonics and Dunkl transforms
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505 0 $a Preface -- Spherical harmonics and Fourier transform -- Dunkl operators associated with reflection groups -- h-Harmonics and analysis on the sphere -- Littlewood–Paley theory and the multiplier theorem -- Sharp Jackson and sharp Marchaud inequalities -- Dunkl transform -- Multiplier theorems for the Dunkl transform -- Bibliography.
520 $a As a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a bare minimum.
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