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Analysis on h-Harmonics and Dunkl Transforms

  • Textbook
  • © 2015

Overview

Authors:
  1. Feng Dai

    1. Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Canada

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  2. Yuan Xu

    1. Department of Mathematics, University of Oregon, Eugene, USA

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    You can also search for this author in PubMed   Google Scholar

Editors:
  1. Sergey Tikhonov

    1. ICREA Research Professor, Campus de Bellaterra, Centre de Recerca Matemàtica, Barcelona, Spain

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  • Focusses on the analysis side of h-harmonics and Dunkl transforms
  • Written in a concise yet informative style
  • No previous knowledge on reflection groups required

Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction: Spherical Harmonics and Fourier Transform

    • Feng Dai, Yuan Xu
    Pages 1-6

  3. Dunkl Operators Associated with Reflection Groups

    • Feng Dai, Yuan Xu
    Pages 7-14

  4. h-Harmonics and Analysis on the Sphere

    • Feng Dai, Yuan Xu
    Pages 15-34

  5. Littlewood–Paley Theory and the Multiplier Theorem

    • Feng Dai, Yuan Xu
    Pages 35-50

  6. Sharp Jackson and Sharp Marchaud Inequalities

    • Feng Dai, Yuan Xu
    Pages 51-63

  7. Dunkl Transform

    • Feng Dai, Yuan Xu
    Pages 65-94

  8. Multiplier Theorems for the Dunkl Transform

    • Feng Dai, Yuan Xu
    Pages 95-109

  9. Back Matter

    Pages 111-118
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Keywords

About this book

​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.

Reviews

“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)

Authors, Editors and Affiliations

  • ICREA Research Professor, Campus de Bellaterra, Centre de Recerca Matemàtica, Barcelona, Spain

    Sergey Tikhonov

  • Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Canada

    Feng Dai

  • Department of Mathematics, University of Oregon, Eugene, USA

    Yuan Xu

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