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.
Rezensionen / Stimmen
"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)
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für Beruf und Forschung
Graduate
Illustrationen
Maße
Höhe: 24 cm
Breite: 16.8 cm
Gewicht
ISBN-13
978-3-0348-0886-6 (9783034808866)
DOI
10.1007/978-3-0348-0887-3
Schweitzer Klassifikation
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.
