Fourier-Stieltjes Transforms which vanish at infinity off certain sets

Abstract

In this paper G is a nondiscrete compact abelian group with character group Г and M ( G ) the usual convolution algebra of Borel measures on G . We designate the following subspaces of M ( G ) employing the customary notations: M a ( G ) those measures which are absolutely continuous with respect to Haar measure; M S ( G ) the space of measures concentrated on sets of Haar measure zero and M d ( G ) the discrete measures.