Sohail Faranghi (Posen)

Abstract:

Birkhoff's pointwise ergodic theorem and the Wiener-Wintner Theorem have been extended to large classes of operators on various function spaces. In this talk we will first explore a recent generalization of the uniform Wiener-Wintner Theorem of Bourgain to the operatorial setting due to the speaker and Barthmann (see https://arxiv.org/abs/2404.05877)External link. This generalization applies to a class of operators satisfying the spaCb condition, which appies in particular to compositions of ergodic Koopman operators with contractive multiplication operators, which is a special case of a Lamperti operator. We will then consider generalizations of these results to Lamperti representations of amenable groups.