Characterizations of measures whose Fourier-Stieltjes transforms vanish at infinity

Fourier Asymptotics of Cantor Type Measures at Infinity

where q ≥ 3 is an integer, then lim t→∞φ(t) > 0. Moreover, the average 1 2T ∫ T −T |φ(t)|dt = O(T log 2 log q ), as T → ∞. Note that φ is the characteristic function of the random variable X = ∑∞ n=1 ρ εn, where {εn}n=1 is a sequence of i.i.d. Bernoulli random variables, and the corresponding distribution is a Cantor type measure. This measure is the most basic model in fractal theory; it is ge...

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

Translation in Measure Algebras and the Correspondence to Fourier Transforms Vanishing at Infinity

Let G denote a locally compact (not necessarily abelian) group and M(G) the collection of finite regular Borel measures on G. The set M(G) is a semisimple Banach algebra with identity under convolution *. It can be identified with the dml space of CO(G), the space of continuous complex-valued functions on G that vanish at infinity, with the sup-norm. The group G has a left-invariant regular Bor...

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.