Hankel transformation of Colombeau type tempered generalized functions
type: Item
instance of: scholarly article
title: Hankel transformation of Colombeau type tempered generalized functions
zbMATH Open document ID: 0915.46037
author: Jorge J. Betancor
author: Lourdes Rodríguez-Mesa
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-06-28T00:00:00Z
review text: The Hankel transformation is defined on a new class \({\mathcal H}_{\mu,\tau}\) of generalized functions of Colombeau type. The space of distributions of slow growth \({\mathcal H}_\mu\) introduced by Zemanian to define the Hankel transformation is contained in \({\mathcal H}_{\mu,\tau}\). Moreover, the introduced Hankel transformation on \({\mathcal H}_{\mu,\tau}\) coincides in a suitable weak sense with the one defined by Zemanian when restricted on the Zemanian slow growth distributions. Some properties of the Hankel transformation as well as the Hankel translation and Hankel convolution on the space \({\mathcal H}_{\mu,\tau}\) are given.
reviewed by: Yuri Luchko
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 1115471
zbMATH Keywords: Hankel transformation
zbMATH Keywords: Hankel convolution
zbMATH Keywords: Zemanian space
zbMATH Keywords: distributions
zbMATH Keywords: generalized functions of Colombeau type
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5705
OpenAlex ID: W2025313658
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DOI: 10.1006/JMAA.1997.5705
description: scientific article; zbMATH DE number 1115471