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Tame L p -multipliers

Kathryn Hare (1993)

Colloquium Mathematicae

We call an L p -multiplier m tame if for each complex homomorphism χ acting on the space of L p multipliers there is some γ 0 ∈ Γ and |a| ≤ 1 such that χ ( γ m ) = a m ( γ 0 γ ) 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 L p -improving tame multipliers which are similar to those obtained for measures, but...

The convolution equation P = P * Q of Choquet and Deny and relatively invariant measures on semigroups

Arunava Mukherjea (1971)

Annales de l'institut Fourier

Choquet and Deny considered on an abelian locally compact topological group the representation of a measure P as the convolution product of itself and a finite measure Q : P = P * Q .In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions P of the above equation which are relatively invariant on the support of Q . A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results on the above convolution...

The Lévy continuity theorem for nuclear groups

W. Banaszczyk (1999)

Studia Mathematica

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...

The Poisson boundary of random rational affinities

Sara Brofferio (2006)

Annales de l’institut Fourier

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 p -adic fileds.

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