Convolution Semigroups Of Probability Measures Research Articles

Cone-Parameter Convolution Semigroups and Their Subordination

Convolution semigroups of probability measures with parameter in a cone in a Euclidean space generalize usual convolution semigroups with parameter in $[0,\infty)$. A characterization of such semigroups is given and examples are studied. Subordination of cone-parameter convolution semigroups by cone-valued cone-parameter convolution semigroups is introduced. Its general description is given and inheritance properties are shown. In the study the distinction between cones with and without strong bases is important.

The arithmetic of a semigroup of series of Walsh functions

AbstractLet be the classical system of the Walsh functions, the multiplicative semigroup of the functions represented by series of functions Wk(t)with non-negative coefficients which sum equals 1. We study the arithmetic of . The analogues of the well-known [ related to the arithmetic of the convolution semigroup of probability measures on the real line are valid in . The classes of idempotent elements, of infinitely divisible elements, of elements without indecomposable factors, and of elements without indecomposable and non-degenerate idempotent factors are completely described. We study also the class of indecomposable elements. Our method is based on the following fact: is isomorphic to the semigroup of probability measures on the groups of characters of the Cantor-Walsh group.

On the uniqueness problem for continuous convolution semigroups of probability measures on simply connected nilpotent Lie groups

On the uniqueness problem for continuous convolution semigroups of probability measures on simply connected nilpotent Lie groups

Representations of Sheffer Polynomials

In this paper we investigate which Sheffer polynomials can be represented as moments of convolution semigroups of probability measures. We also obtain general integral representations for shift‐invariant operators and for umbral operators. As a corollary, we obtain new proofs for representation theorems for Sheffer polynomials due to Sheffer and Thorne.

Tail behavior for semigroups of measures on groups

Let (μt)t>0 be a convolution semigroup of probability measures on a measurable group (G, ℬ). In this paper, we provide precise information about the asymptotic behavior of μt{q>s, whereq is a measurable seminorm and (μt)t>0 isq-continuous.

Hemigroups of probability measures on a locally compact group

In contrast to the widely elaborated theory of continuous convolution semigroups of probability measures on a locally compact group G there are only a few results concerning two-parameter semigroups of probability measures («hemigroups»), i.e. families (μ(s,t)) 0≤s≤t of probability measures on G such that (s,t)→μ(s,t) is weakly continous, μ(t,t) is the Dirac measure in the identity of G and μ(r,s)*μ(s,t)=μ(r,t) holds for all 0≤r≤s≤t. We discuss the characterization and generation of continuous hemigroups of probability measures on not necessarily abelian or compact locally compact groups by families of generators of continous convolution semigroups. Our results are based on the corresponding results for evolution families

Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups

Let (μ t ) t⪖0 be a τ-semistable convolution semigroup of probability measures on a Lie groupG whose idempotentμ 0 is the Haar measure on some compact subgroupK. Then all the measuresμ 1 are supported by theK-contraction groupC K(τ) of the topological automorphism τ ofG. We prove here the structure theoremC K(τ)=C(τ)K, whereC(τ) is the contraction group of τ. Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.

Uniform semigroups and fixed point properties

LetS be a uniform semigroup (this includes all topological groups and affine semigroups). We show that a certain space of uniformly continuous functions onS has a left invariant mean iffS has the fixed point property for uniformly continuous affine actions ofS on compact convex sets. This is closely related to but independent of the results of T. Mitchell in [13] and A. Lau in [10]. Interesting examples and consequences are given for the special cases of topological groups and affine convolution semigroups of probability measures on a locally compact semigroup or group.

Analytische Vektoren von Faltungshalbgruppen II. Funktionenr�ume, auf lokalkompakten Gruppen

In this paper the investigations of [3], [4], [5] are continued. LetG be a locally compact group. First we show that in general there is no rich subspace of functions of the Bruhat-spaceD (G), whose, elements are analytical vectors for any convolution semigroup of probability measures. On the other hand we are able to construct dense subspaces ofC0 (G) of analytical vectors, ifG is a Moore-group or a symmetric Riemannian space. We study properties of these subspaces and their relations to the structure, of the groupG.

Symmetrische Gaussverteilungen sind diffus

Let G be a locally compact topological group and let be a weakly continuous one parameter convolution semigroup of probability measures on G. Suppose, that each measure is normal, i.e. commutes with the adjoint measure. Then the symmetric part is also a continuous one parameter convolution semigroup.

On central primitive idempotent measures

Let S be a compact semitopological semigroup and let P(S) be the convolution semigroup of probability measures on S. An idempotent measure μ in P(S) is defined to be primitive if and only idempotent measures in μP(S)μ are μ and the zero element m of P(S). In a previous paper [2] we give some characterization of primitive idempotent measures on S. Let Π(P(S)) be the set of primitive idempotents in P(S) and let Πc be the set of central primitive idempotents in P(S). It is shown in [1] that Π(P(S)) is neither an ideal nor even a subsemigroup of P(S) in general. The purpose of this paper is to investigate the structure of Πc.