Analysis on h-Harmonics and Dunkl Transforms

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Analysis on h-Harmonics and Dunkl Transforms

フォーマット:
電子ブック
責任表示:
by Feng Dai, Yuan Xu ; edited by Sergey Tikhonov
本文言語:
英語
出版情報:
Basel, Switzerland. 2015-. Springer Basel,Imprint: Birkhäuser
シリーズ:
Advanced Courses in Mathematics - CRM Barcelona
概要:
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. 続きを見る
目次:
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.
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
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1.
Excursions in Harmonic Analysis, Volume 3 : The February Fourier Talks at the Norbert Wiener Center by Balan, Radu; Begué, Matthew J; Benedetto, John J; Czaja, Wojciech; Okoudjou, Kasso A; SpringerLink
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3.
Excursions in Harmonic Analysis, Volume 4 : The February Fourier Talks at the Norbert Wiener Center by Balan, Radu; Begué, Matthew; Benedetto, John J; Czaja, Wojciech; Okoudjou, Kasso A; SpringerLink
4.
Excursions in Harmonic Analysis, Volume 5 : The February Fourier Talks at the Norbert Wiener Center by Balan, Radu; Benedetto, John J; Czaja, Wojciech; Dellatorre, Matthew; Okoudjou, Kasso A; SpringerLink
5.
Sparse Approximation with Bases by Temlyakov, Vladimir; Tikhonov, Sergey; SpringerLink
6.
Fourier Analysis and Approximation of Functions by Trigub, Roald M; Bellinsky, Eduard S; SpringerLink
7.
The Mellin Transformation and Fuchsian Type Partial Differential Equations by Szmydt, Zofia; Ziemian, Bogdan; SpringerLink
8.
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9.
Approximation with Positive Linear Operators and Linear Combinations by Gupta, Vijay; Tachev, Gancho; SpringerLink
10.
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