E28

The present talk is based on my Ph.D. dissertation and consists of two more or less independent topics. First we investigate questions concerning Gauss measures on special noncommutative Lie groups, such as on the Heisenberg group and on the affine group. Then we deal with proving (central) limit theorems for infinitesimal triangular arrays of random elements with values in (special) locally compact Abelian topological groups. In case of the 3-dimensional Heisenberg group an explicit formula is derived for the Fourier transform of a Gauss measure at the Schrödinger representations. Using this explicit formula, we give necessary and sufficient conditions for the convolution of two Gauss measures to be a Gauss measure. It turns out that the convolution of Gauss measures on the Heisenberg group is almost never a Gauss measure. In case of the affine group F it is shown that a Gauss measure on F can be embedded only in a uniquely determined Gauss semigroup. Moreover, we give a complete description of supports of Gauss measures on the affine group using Siebert`s support formula. Concerning limit theorems on locally compact Abelian topological groups first we recall the most important notions and known results in the theory. As new results we prove necessary and sufficient conditions for convergence of the row sums of symmetric arrays, where the limit measure can also be a nondegenerate normalized Haar measure on a compact subgroup. Then we investigate special Abelian topological groups: the group of p-adic integers and the p-adic solenoid.

Tee: 15.45 Uhr, Raum 614/616

Dr. Mátyás Barczy

University of Debrecen, Ungarn