Inversion of the Dunkl intertwining operator and its dual using Dunkl wavelets.
type: Item
instance of: scholarly article
title: Inversion of the Dunkl intertwining operator and its dual using Dunkl wavelets.
zbMATH Open document ID: 1034.44005
author: Khalifa Trimèche
published in: Rocky Mountain Journal of Mathematics
publication date: 2003-12-03T00:00:00Z
full work available at URL: CONT32-2.html
review text: In \S1 of the paper, the author gives results on the Dunkl operators and on eigenfunction called the Dunkl kernel and then he defines the Dunkl intertwining operator \(V_k\) and its dual \({}^tV_k\) and mentions their main properties. In Sections 3 and 4, the harmonic analysis associated with Dunkl operators (Dunkl transform, Dunkl translation operators and Dunkl convolution product) are studied, while in the fifth section the author gives spaces other than \({\mathcal E}(\mathbb{R}^d)\) and \({\mathcal D}(\mathbb{R}^d)\) on which the Dunkl intertwining operator \(V_k\) and its dual \({}^tV_k\) are bijective and establishes inversion formulas for these operators. Next he defines and studies Dunkl wavelets and Dunkl continuous wavelet transform and then Plancherel and inversion formulas are given for this transform. Finally using Dunkl wavelets, formulas which give the inverse operators of the operators \(V_k\) and \({}^tV_k\) are obtained.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 2012121
zbMATH Keywords: Dunkl operators
zbMATH Keywords: inversion
zbMATH Keywords: Dunkl kernel
zbMATH Keywords: wavelet transform
zbMATH Keywords: Plancherel formula
zbMATH Keywords: intertwining operator
zbMATH Keywords: Dunkl transform
zbMATH Keywords: Dunkl translation operators
zbMATH Keywords: Dunkl convolution product
zbMATH Keywords: Dunkl wavelets
MaRDI profile type: Publication
OpenAlex ID: W1979198036
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DOI: 10.1216/RMJM/1030539700
description: scientific article; zbMATH DE number 2012121