A Birkhoff theorem for Riemann surfaces
Let \(R\) be a noncompact Riemann surface and \(\{\phi_n\}_{n \geq 0}\) be a sequence of holomorphic self-mappings of \(R\). This paper is devoted to the generalization of the following classical Birkhoff theorem on \(R\): there exists an entire function \(f\) such that the sequence \(\{f(z+n))\}_{n \geq 0}\) is dense in the space of entire functions. The author shows (Theorem 3.1) when there exists a holomorphic function \(f\) on \(R\) such that \(\{f \circ \phi_n\}_{n \geq 0}\) is dense in the space of holomorphic functions on \(R\). Besides that there are considered some connections with this questions.
scientific article; zbMATH DE number 1309738