Dynamics of weighted composition operators on spaces of entire functions of exponential and infraexponential type

Abstract

Given an affine symbol φ and a multiplier w, we focus on the weighted composition operator Cw,φ acting on the spaces Exp and Exp0 of entire functions of exponential and of infraexponential type, respectively. We characterize the continuity of the operator and, for w the product of a polynomial by an exponential function, we completely characterize power boundedness and (uniform) mean ergodicity. In the case of multiples of composition operators, we also obtain the spectrum and characterize hypercyclicity.