Analysis on h-Harmonics and Dunkl Transforms [Paperback]

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.Preface.- Spherical harmonics and Fourier transform.- Dunkl operators associated with reflection groups.- h-Harmonics and analysis on the sphere.- LittlewoodPaley theory and the multiplier theorem.- Sharp Jackson and sharp Marchaud inequalities.- Dunkl transform.- Multiplier theorems for the Dunkl transform.- Bibliography.

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

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 transfolÃ)