Stable invariant measures in linear dynamics

Abstract

We study the existence of stable invariant measures for operators and strongly continuous semigroups of operators on Banach spaces admitting either a dense bilateral backward orbit or a sufficiently rich family of eigenvectors. These invariant measures are realized as the distributions of stochastic integrals with respect to stable random measures. We also discuss invariant measures with other classes of distributions for such operators and semigroups.

28 pages