Dynamics of weighted composition operators on weighted Banach spaces of entire functions

We study the dynamics of the weighted composition operator C-omega,C-phi on weighted Banach spaces of entire functions H-v (C) and H-v(0) (C). We characterize the continuity and compactness of the operator and, in the case of affine symbols phi(z) = az + b, a, b is an element of C, and exponential weights, we analyze when the operator is power bounded, (uniformly) mean ergodic and hypercyclic. Continuous weighted composition operators when vertical bar a vertical bar = 1 are just multiples of composition operators lambda C-phi lambda is an element of C. When vertical bar a vertical bar < 1, we consider as a multiplier omega the product of a polynomial by an exponential function. For multiples of composition operators, we get a complete characterization of power boundedness and mean ergodicity and we study the hypercyclicity in terms of lambda. An example of a power bounded but not mean ergodic operator on H-v(0) (C) is provided. For the case of composition operators, we obtain the spectrum and a complete characterization of the dynamics. (C) 2020 Elsevier Inc. All rights reserved.