Displaying similar documents to “The convolution equation P = P * Q of Choquet and Deny and relatively invariant measures on semigroups”

Pointwise estimates for densities of stable semigroups of measures

Paweł Głowacki, Waldemar Hebisch (1993)

Studia Mathematica

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Let μ t be a symmetric α-stable semigroup of probability measures on a homogeneous group N, where 0 < α < 2. Assume that μ t are absolutely continuous with respect to Haar measure and denote by h t the corresponding densities. We show that the estimate h t ( x ) ≤ t Ω ( x / | x | ) | x | - n - α , x≠0, holds true with some integrable function Ω on the unit sphere Σ if and only if the density of the Lévy measure of the semigroup belongs locally to the Zygmund class LlogL(N╲e). The problem turns out to be related to the properties...

On systems of imprimitivity on locally compact abelian groups with dense actions

J. Mathew, M. G. Nadkarni (1978)

Annales de l'institut Fourier

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Consider the four pairs of groups ( Γ , R ) , ( Γ / Γ 0 , R / Γ 0 ) , ( K ∩ S , P ) and ( S , B ) , where Γ , R are locally compact second countable abelian groups, Γ is a dense subgroup of R with inclusion map from Γ to R continuous; Γ 0 ⊆ Γ ⊆ R is a closed subgroup of R ; S , B are the duals of R and Γ respectively, and K is the annihilator of Γ 0 in B . Let the first co-ordinate of each pair act on the second by translation. We connect, by a commutative diagram, the systems of imprimitivity which arise in a natural fashion on each pair, starting...

On concentrated probabilities on non locally compact groups

Wojciech Bartoszek (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a Polish group with an invariant metric. We characterize those probability measures μ on G so that there exist a sequence g n ∈ G and a compact set A ⊆ G with   μ * n ( g n A ) ≡ 1   for all n .