Wiener Tauberian theorems for vector-valued functions

K. Parthasarathy and Sujatha Varma

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-4

Abstract:

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 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.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:165648

DOI: 10.1155/S0161171294000694

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