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International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 475-478

Wiener Tauberian theorems for vector-valued functions

1Ramanujan Institute, University of Madras, Madras 600 005, India
2School of Sciences, Indira Gandhi National Open University, New Delhi 110 068, India

Received 24 April 1991; Revised 19 April 1993

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.