Stability in the I. V. Ostrovskii-R. Cuppens theorem on groups

Abstract

Let X be a locally compact separable metric Abelian group. Unimprovable estimates are obtained for the stability of the decompositions of the generalized Poisson distribution e(F) on X, where F is a completely finite measure on X such that its powers fn* with respect to convolution are pairwise singular for distinct natural numbers n.