Probability Measures on Groups IX [electronic resource] : Proceedings of a Conference held in Oberwolfach, FRG, January 17–23, 1988 / edited by Herbert Heyer.

A Fourier-analytic proof that conditional probability distributions exist on a group -- Tauberian theorems in probability theory -- Characterisation of potential kernels of transient convolution semigroups on a commutative hypergroup -- Embedding infinitely divisible probablities on the affine group -- A propos de l'induction des convoluteurs -- Characterization of the type of some generalizations of the cauchy distribution -- Operators, stochastic processes, and lie groups -- Rectification à l'article de L. Gallardo et O. Gebuhrer "Lois de probabilités infiniment divisibles sur les hypergroupes commutatifs discrets dénombrables" (Probability Measures on Groups VII Lecture Notes 1064) -- Convergence-of-types theorem for simply connected nilpotent lie groups -- MD-semigroups, decomposition of point processes, central limit theorems for certain T2-semigroups -- Infinite dimensional rotation group and unitary group -- A note on the semigroup of analytic mappings with a common fixed point -- Localizations of Feller infinitesimal generators and uniqueness of corresponding killed processes -- A dichotomy theorem for random walks on hypergroups -- A modification of stationarity for stochastic processes induced by orthogonal polynomials -- Le problem de la classification des familles exponentielles naturelles de ?d ayant une fonction variance quadratique -- Convolution products of non-identical distributions on a compact Abelian semigroup -- The Levy Laplacian and mean value theorem -- Bimeasures and harmonizable processes (Analysis, classification, and representation) -- A conjecture concerning mixtures of characters from a given closed subsemigroup in the dual -- Infinitely divisible states on cocommutative bialgebras -- Semistable convolution semigroups and the topology of contraction groups -- The central limit theorem for the symmetric space of GL(3) -- Roots of haar measure and topological hamiltonian groups -- Negative definite functions on commutative hypergroups -- Lp-improving measures on hypergroups -- Statistics of rotations -- Completely bounded and related random fields on locally compact groups -- On the max-divisibility of two dimensional normal random variables -- Properties of the cosh hypergroup.

The latest in this series of Oberwolfach conferences focussed on the interplay between structural probability theory and various other areas of pure and applied mathematics such as Tauberian theory, infinite-dimensional rotation groups, central limit theorems, harmonizable processes, and spherical data. Thus it was attended by mathematicians whose research interests range from number theory to quantum physics in conjunction with structural properties of probabilistic phenomena. This volume contains 5 survey articles submitted on special invitation and 25 original research papers.