Wiener Tauberian theorems for vector-valued functions

Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(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 Wiener...

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Main Authors: K. Parthasarathy, Sujatha Varma
Format: Article
Language:English
Published: Wiley 1994-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171294000694
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author K. Parthasarathy
Sujatha Varma
author_facet K. Parthasarathy
Sujatha Varma
author_sort K. Parthasarathy
collection DOAJ
description Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(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 Wiener's Tauberian property is introduced and it is proved that L1(G,A) is weakly Tauberian if and only if A is. The vector analogue of Wiener's L2-span of translates theorem is examined.
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spelling doaj-art-665a5b8ee22f49cc877132de65c810dd2025-08-20T02:23:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117347547810.1155/S0161171294000694Wiener Tauberian theorems for vector-valued functionsK. Parthasarathy0Sujatha Varma1Ramanujan Institute, University of Madras, Madras 600 005, IndiaSchool of Sciences, Indira Gandhi National Open University, New Delhi 110 068, IndiaDifferent versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(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 Wiener's Tauberian property is introduced and it is proved that L1(G,A) is weakly Tauberian if and only if A is. The vector analogue of Wiener's L2-span of translates theorem is examined.http://dx.doi.org/10.1155/S0161171294000694generalized group algebraWiener's Tauberian property.
spellingShingle K. Parthasarathy
Sujatha Varma
Wiener Tauberian theorems for vector-valued functions
International Journal of Mathematics and Mathematical Sciences
generalized group algebra
Wiener's Tauberian property.
title Wiener Tauberian theorems for vector-valued functions
title_full Wiener Tauberian theorems for vector-valued functions
title_fullStr Wiener Tauberian theorems for vector-valued functions
title_full_unstemmed Wiener Tauberian theorems for vector-valued functions
title_short Wiener Tauberian theorems for vector-valued functions
title_sort wiener tauberian theorems for vector valued functions
topic generalized group algebra
Wiener's Tauberian property.
url http://dx.doi.org/10.1155/S0161171294000694
work_keys_str_mv AT kparthasarathy wienertauberiantheoremsforvectorvaluedfunctions
AT sujathavarma wienertauberiantheoremsforvectorvaluedfunctions