Analysis on h-Harmonics and Dunkl Transforms

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.

List 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.

Report

"This well-written book gives a readable introduction to Dunkl harmonics and Dunkl transforms ... . the authors have collected a small compendium of results which will appeal to mathematicians interested in Dunkl analysis. ... The authors have done a commendable job in making this little book self-contained and quite readable. It will certainly serve as a starting point for graduate students and researchers interested in learning Dunkl harmonics and Dunkl transforms." (Sundaram Thangavelu, Mathematical Reviews, December, 2015)

Product details

• Authors: Feng Dai, Yuan Xu
• Assisted by: Sergey Tikhonov (Editor)
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 13.02.2015
• EAN: 9783034808866
• ISBN: 978-3-0-3480886-6
• No. of pages: 118
• Dimensions: 170 mm x 240 mm x 10 mm
• Illustrations: VIII, 118 p.
• Series: Advanced Courses in Mathematics - CRM Barcelona
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Mathematics and Statistics, Functional Analysis, Complex analysis, complex variables, Abstract Harmonic Analysis, Harmonic analysis, Operational calculus, Integral transforms, Integral Transforms and Operational Calculus, Integral Transforms, Operational Calculus, Integral calculus & equations, Functional analysis & transforms, Approximations and Expansions, Approximation theory