Convolution over the spaces \({\mathcal S}'_k\)
type: Item
instance of: scholarly article
title: Convolution over the spaces \({\mathcal S}'_k\)
zbMATH Open document ID: 0827.46035
author: B. González
author: E. R. Negrin
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-06-08T00:00:00Z
review text: The authors prove that for \(f\in {\mathcal S}_k'\) and \(g\in {\mathcal S}_k'\), \(k\in \mathbb{Z}\), \(k<0\), the extension from \({\mathcal D}\) to \({\mathcal S}_k\) of the convolution \(f* g\), defined according to the lines of Schwartz, Horváth, and Dierolf and Voigt, agrees with the functional \(f\# g\in {\mathcal S}_k'\), given by \(\langle f(x), \langle g(y), \varphi(x+ y)\rangle \rangle\), \(\varphi\in {\mathcal S}_k\), where \({\mathcal S}_k'\) is the dual of the space \({\mathcal S}_k\) introduced by Horváth.
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 762194
zbMATH Keywords: convolution
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1115
OpenAlex ID: W1977916878
DOI: 10.1006/JMAA.1995.1115
description: scientific article; zbMATH DE number 762194