Fourier-Stieltjes transforms of strongly continuous measures.

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...

Surface Measures - Maximal Functions and Fourier Transforms

Continuous quaternion fourier and wavelet transforms

It is well-known that every two dimensional rotation around the origin in the plane R can be represented by the multiplication of the complex number e = cos θ + i sin θ, 0 ≤ θ < 2π. Similarly, every three dimensional rotation in the space R can be represented by the multiplications of the quaternion q from the left-hand side and its conjugate q̄ from the right-hand side, where q = cos(θ/2) + α s...

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 Remark on Circular Means of Fourier Transforms of Measures

In [7] the optimal decay of circular L means of compactly supported measures of finite energy was given for p ≥ 2, with application to Falconer’s distance problem. The question was then raised in that paper as to whether any non-trivial improvement to these estimates were available for p < 2. We answer this question in the negative. This paper is concerned with the quantity σp(α) defined by Wol...