Wiener Tauberian Theorems for Vector - Valued Functions
نویسنده
چکیده
Different versions of Wiener’s Tauberian theorem are discussed for the generalized group algebra LI(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 LI(G,A) is weakly Tauberian if and only if A is. The vector analogue of Wiener’s L-span of translates theorem is examined.
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