The moment problem on divisible abelian semigroups

On Compact Divisible Abelian Semigroups

The algebraic structure of divisible abelian semigroups has been studied in [9] and [l]. Some results on the topological and algebraic structure of compact uniquely divisible abelian semigroups have been obtained in [4] and [5]. A statement of equivalent conditions for a compact abelian semigroup to be divisible is presented in the present paper. Some of the results in [4] are extended to subun...

On in nitely divisible solutions to indeterminate moment problems

Weakly infinitely divisible measures on some locally compact Abelian groups

Let G be a locally compact Abelian topological group having a countable basis of its topology. We also suppose that G has the T0–property, that is, ⋂ U∈Ne U = {e}, where e denotes the identity element of G and Ne is the collection of all Borel neighbourhoods of e. (By a Borel neighbourhood U of e we mean a Borel subset of G for which there exists an open subset Ũ of G such that e ∈ Ũ ⊂ U.) Let ...

Truncated Moment Problem versus Moment Problem 3

It is shown that the truncated multidimensional moment problem is more general than the full multidimensional moment problem.

Growth of sumsets in abelian semigroups

Let S be an abelian semigroup, written additively, that contains the identity element 0. Let A be a nonempty subset of S. The cardinality of A is denoted |A|. For any positive integer h, the sumset hA is the set of all sums of h not necessarily distinct elements of A. We define hA = {0} if h = 0. Let A1, . . . , Ar, and B be nonempty subsets of S, and let h1, . . . , hr be nonnegative integers....