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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Graduate
Illustrationen
ISBN-13
978-3-0348-0887-3 (9783034808873)
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.
