Weighted composition operators on Fock spaces and their dynamics

Abstract

Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined in terms of the order and type of the multiplier, and a complete description of zero-free multipliers is obtained. Explicit asymptotics for iterates of such operators are given. As an application, the question of whether weighted composition operators on the Fock space can be supercyclic is answered in the negative.