Unbounded translation invariant operators on locally compact abelian groups
type: Item
instance of: scholarly article
title: Unbounded translation invariant operators on locally compact abelian groups
zbMATH Open document ID: 0840.43015
author: Dirk Alboth
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-01T00:00:00Z
review text: Let \(T : D(T) \subseteq L_p (G) \to L_p (G)\) be a densely defined linear operator. \(T\) is called translation invariant if and only if \(T\) is closable and commutes with translations. The author characterizes translation invariant operators on \(L_1 (G)\) and \(L_2 (G)\), where \(G\) is a locally compact abelian group. Also, he considers their relationship to translation invariant operators on \(L_p (G)\)-spaces.
Mathematics Subject Classification ID: 43A70
Mathematics Subject Classification ID: 22B05
Mathematics Subject Classification ID: 43A15
zbMATH DE Number: 811182
zbMATH Keywords: linear operator
zbMATH Keywords: translation invariant
zbMATH Keywords: locally compact abelian group
reviewed by: Bolis Basit
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1245
OpenAlex ID: W2068677694
DOI: 10.1006/JMAA.1995.1245
description: scientific article; zbMATH DE number 811182