Analysis on h-Harmonics and Dunkl Transforms

Analysis on h-Harmonics and Dunkl Transforms

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 we...

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Bibliographic Details
Published in:Springer eBooks
Main Authors: Dai, Feng (Author), Xu, Yuan (Author)
Corporate Author: SpringerLink (Online service)
Other Authors: Tikhonov, Sergey (Editor)
Format: eBook
Language:English
Published: Basel : Springer Basel : Imprint: Birkhäuser, 2015.
Series:Advanced Courses in Mathematics - CRM Barcelona,
Subjects:
mathematics.
Harmonic analysis.
Approximation theory.
Functional analysis.
Integral Transforms.
Operational calculus.
Mathematics.
Approximations and Expansions.
Abstract Harmonic Analysis.
Integral Transforms, Operational Calculus.
Functional Analysis.
Online Access:http://dx.doi.org/10.1007/978-3-0348-0887-3
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Table of Contents:
  • 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.

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