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 K. Parthasarathy and Sujatha Varma. 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 (of integrable functions on a locally compact abelian group taking values in a commutative semisimple regular Banach algebra ) using -valued Fourier transforms. A weak form of Wiener's Tauberian property is introduced and it is proved that is weakly Tauberian if and only if is. The vector analogue of Wiener's -span of translates theorem is examined.