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Analysis on h-Harmonics and Dunkl Transforms (Advanced Courses in Mathematics - CRM Barcelona)

De (autor) , Editat de Sergey Tikhonov
Notă GoodReads:
en Limba Engleză Carte Paperback – 13 Feb 2015
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.
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Specificații

ISBN-13: 9783034808866
ISBN-10: 3034808860
Pagini: 125
Ilustrații: Bibliographie
Dimensiuni: 168 x 240 x 15 mm
Greutate: 0.26 kg
Ediția: 2015
Editura: Springer
Colecția Birkhäuser
Seria Advanced Courses in Mathematics - CRM Barcelona

Locul publicării: Basel, Switzerland

Public țintă

Graduate

Recenzii

“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)

Textul de pe ultima copertă

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.

Caracteristici

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