Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual
type: Item
instance of: scholarly article
title: Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual
zbMATH Open document ID: 1090.42023
DOI: 10.1155/S0161171204212285
author: Abdellatif Jouini
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/52441
review text: The author considers the Dunkl operator \(\Lambda_\alpha\) on \(\mathbb{R}\) of index \((\alpha+{1\over 2})\), \(\alpha>-{1\over 2}\), associated with the reflection group \(\mathbb{Z}_2\) given by \[ \Lambda_\alpha u(x)={d\over dx} u(x)+ {\alpha+{1\over 2}\over x} [u(x)+ u(- x)]. \] He studies the Dunkl wavelet and the corresponding Dunkl wavelet transforms, and he proves for these transforms Plancherel and reconstruction formulas. As applications of these results he deduces the relations which give the inverse operators of the Dunkl intertwining operator and of its dual.
reviewed by: Khalifa Trimèche
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 2168612
zbMATH Keywords: Dunkl wavelets
zbMATH Keywords: Dunkl intertwinning operator
MaRDI profile type: Publication
OpenAlex ID: W2140835881
description: scientific article; zbMATH DE number 2168612