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Universal functions for composition operators. (English) Zbl 0838.30032

Let \(H(\Omega)\) be the space of analytic functions on a complex region \(\Omega\). In this paper, we characterize the sequences \(\{\varphi_n\}_{n\geq 1}\) of automorphisms of \(\Omega\) with the following property: There exists \(f\in H(\Omega)\) (in fact, a residual set of them) such that the orbit \(\{f\circ \varphi_n\}_{n\geq 1}\) is dense in \(H(\Omega)\). Some known results (as, for instance, Birkhoff’s theorem) are derived and some new others are obtained.

MSC:

30E10 Approximation in the complex plane
47B38 Linear operators on function spaces (general)
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