Analysis on h-Harmonics and Dunkl Transforms

• Main Authors: Dai, Feng (Author), Xu, Yuan (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Tikhonov, Sergey (Editor)
• Format: Electronic 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.; Approximations and Expansions.; Abstract Harmonic Analysis.; Integral Transforms, Operational Calculus.; Functional Analysis.

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...

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.