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We call an -multiplier m tame if for each complex homomorphism χ acting on the space of multipliers there is some and |a| ≤ 1 such that for all γ ∈ Γ. Examples of tame multipliers include tame measures and one-sided Riesz products. Tame multipliers show an interesting similarity to measures. Indeed we show that the only tame idempotent multipliers are measures. We obtain quantitative estimates on the size of -improving tame multipliers which are similar to those obtained for measures, but...
Choquet and Deny considered on an abelian locally compact topological group the representation of a measure as the convolution product of itself and a finite measure .In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions of the above equation which are relatively invariant on the support of . A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results on the above convolution...
Let G be an abelian topological group. The Lévy continuity theorem says that if G is an LCA group, then it has the following property (PL) a sequence of Radon probability measures on G is weakly convergent to a Radon probability measure μ if and only if the corresponding sequence of Fourier transforms is pointwise convergent to the Fourier transform of μ. Boulicaut [Bo] proved that every nuclear locally convex space G has the property (PL). In this paper we prove that the property (PL) is inherited...
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.
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