A Note on Fourier-Stieltjes Transforms

Representation of Functions as Absolutely Convergent Fourier-stieltjes Transforms

0. Introduction. Let G be a locally compact Abelian group, and G* its group of (continuous) characters. We write (y, x) to indicate the function on G*XG which is the value of the character y EG* at the point *6G, or, dually, the value of the character xEG at the point y EG*. Borel sets in G are taken to be the smallest cr-algebra of sets containing all closed sets. We consider the set of all re...

Some notes on L-projections on Fourier-Stieltjes algebras

In this paper, we investigate the relation between L-projections and conditional expectations on subalgebras of the Fourier Stieltjes algebra B(G), and we will show that compactness of G plays an important role in this relation.

Stieltjes Transforms on New Generalized Functions

We introduce a Stieltjes transform on the equivalence classes of a new generalized function which has been successfully developed by Colombeau. Subsets of rapid descent test functions, (Rn), as well as tempered distributions, ′(Rn), are used to preserve Fourier analysis techniques. 2000 Mathematics Subject Classification. Primary 46F12.

SPECTRUM OF THE FOURIER-STIELTJES ALGEBRA OF A SEMIGROUP

For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

A note on the comparison between Laplace and Sumudu transforms