Analysis on h-Harmonics and Dunkl Transforms

Erscheinungsjahr 2015
ISBN: 978-3-0348-0886-6
Verlag: Birkhäuser

Buch, Englisch, 118 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 254 g

Reihe: Advanced Courses in Mathematics - CRM Barcelona

This book provides an 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 authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms.
Graduate students and researchers working in approximation theory, harmonic analysis, and functional analysis will benefit from this book.

Zielgruppe

Graduate

Autoren/Hrsg.

Xu, Yuan

Dai, Feng

Tikhonov, Sergey

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

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.