Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series

Abstract

A criterion for boundedness of composition operators acting on a class of Hilbert spaces of entire Dirichlet series, namely the class ℋ(E, β ) , was obtained in Hou et al. (J. Math. Anal. Appl. 401: 416–429, 2013) for those spaces that do not contain non-zero constant functions, while other possibilities were not studied. In this paper, we first provide a complete characterization of boundedness of composition operators on any space ℋ(E, β ) , which may or may not contain constant functions. We then study complex symmetry of composition operators on ℋ(E, β ) , via analysis of composition conjugations.