Dynamics of weighted composition operators and their adjoints on the Fock space

Abstract

We study the cyclic structures of the weighted composition operators and their adjoints on the Fock space F2. A complete characterization of cyclicity which depends on the derivative of the symbol for the composition operator and non-vanishing structure of the weight function is provided. It is further shown that the space fails to support supercyclic adjoint weighted composition operators. As a tool in proving our main results, we also identified eigenvectors of the weighted composition operators in the space which is interest of its own.