Wiener Tauberian theorems for vector-valued functions
type: Item
instance of: scholarly article
title: Wiener Tauberian theorems for vector-valued functions
zbMATH Open document ID: 0830.43008
DOI: 10.1155/S0161171294000694
author: Sujatha Varma
author: K. Parthasarathy
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1994-10-09T00:00:00Z
full work available at URL: https://eudml.org/doc/47338
full work available at URL: issue-3.html
review text: Summary: Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebra \(L^1 (G,A)\) (of integrable functions on a locally compact abelian group \(G\) taking values in a commutative semisimple regular Banach algebra \(A)\) using \(A\)-valued Fourier transforms. A weak form of a Wiener's Tauberian property is introduced and it is proved that \(L^1 (G,A)\) is weakly Tauberian if and only if \(A\) is. The vector analogue of Wiener's \(L^2\)-span of translates theorem is examined.
Mathematics Subject Classification ID: 43A20
Mathematics Subject Classification ID: 43A45
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 650817
zbMATH Keywords: Wiener's Tauberian theorem
zbMATH Keywords: integrable functions
zbMATH Keywords: locally compact abelian group
zbMATH Keywords: weakly Tauberian
MaRDI profile type: Publication
OpenAlex ID: W1996346714
description: scientific article; zbMATH DE number 650817