Hilbert spaces of entire Dirichlet series and composition operators (Q1941371)

This paper studies composition operators of the space of entire Dirichlet series with real frequencies. The space of entire Dirichlet series with real frequencies is given by the set of analytic functions \[ \sum_{n=1}^\infty a_n e^{-\lambda_n z} \] with \(a_n,z\in\mathbb{C}\) and \(0\leq\lambda_n\) with \(\lambda_n\to\infty\). The authors determine necessary and sufficient conditions for such series to have Ritt order zero and finite logarithmic orders. Using these, they obtain a characterization of when composition operators on these spaces are compact and bounded.