Complex Symmetry of Composition Operators on Hilbert Spaces of Entire Dirichlet Series

A criterion for boundedness of composition operators acting on a class of Hilbert spaces of entire Dirichlet series, namely the class H(E,beta S), 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,beta S), which may or may not contain constant functions. We then study complex symmetry of composition operators on H(E,beta S), via analysis of composition conjugations.