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Analysis on H-Harmonics and Dunkl Transforms - (Advanced Courses in Mathematics - Crm Barcelona) by Feng Dai & Yuan Xu (Paperback)
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Highlights
- This book provides an introduction to h-harmonics and Dunkl transforms.
- Author(s): Feng Dai & Yuan Xu
- 118 Pages
- Mathematics, Mathematical Analysis
- Series Name: Advanced Courses in Mathematics - Crm Barcelona
Description
Book Synopsis
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.From the Back Cover
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 transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform.
The authors' focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a bare minimum.Review Quotes
"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)
