Wavelets and generalized windowed transforms associated with the Dunkl-Bessel-Laplace operator on \(\mathbb{R}^d \times \mathbb{R}_{+}\)
type: Item
instance of: scholarly article
title: Wavelets and generalized windowed transforms associated with the Dunkl-Bessel-Laplace operator on \(\mathbb{R}^d \times \mathbb{R}_{+}\)
zbMATH Open document ID: 1329.42036
author: Amina Hassini
author: Khalifa Trimèche
published in: Mediterranean Journal of Mathematics
publication date: 2015-11-18T00:00:00Z
review text: The authors describe some properties of the Dunkl-Bessel-Laplace operator \(\Delta_{k,\beta}\) which is a special partial differential-difference operator. Corresponding to \(\Delta_{k,\beta}\), a translation operator and a convolution is introduced. For the Dunkl-Bessel transform, an inversion formula and a Plancherel-type theorem are presented. Associated with \(\Delta_{k,\beta}\), Gaussian wavelets are constructed.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 33E30
zbMATH DE Number: 6510995
zbMATH Keywords: Dunkl-Bessel-Laplace operator
zbMATH Keywords: partial differential-difference operator
zbMATH Keywords: translation operator
zbMATH Keywords: convolution
zbMATH Keywords: Dunkl-Bessel transform
zbMATH Keywords: Gaussian wavelets
reviewed by: Manfred Tasche
MaRDI profile type: Publication
full work available at URL: s00009-015-0540-4
OpenAlex ID: W1987123414
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DOI: 10.1007/S00009-015-0540-4
description: scientific article; zbMATH DE number 6510995