Composition operators on Hilbert spaces of entire functions

Abstract

We obtain a complete description of families of continuous and compact composition operators on Hilbert spaces of entire functions. These operators were introduced by K. Chan and J. Shapiro for studying some dynamic properties of translation operators. In contrast to recent papers devoted to the same problems, we make no additional assumptions on the mentioned spaces. We apply a new research approach based on the embedding of a Hilbert space under consideration into some appropriate Banach space with the sup-norm.