Universal sequences of composition operators

Stéphane Charpentier; Augustin Mouze

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arXiv · 2111.05165

Universal sequences of composition operators

Stéphane Charpentier·Augustin Mouze

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Abstract

Let $G$ and $\Omega$ be two planar domains. We give necessary and sufficient conditions on a sequence $(\phi_n)$ of eventually injective holomorphic mappings from $G$ to $\Omega$ for the existence of a function $f\in H(\Omega)$ whose orbit under the composition by $(\phi_n)$ is dense in $H(G)$. This extends a result of the same nature obtained by Grosse-Erdmann and Mortini when $G=\Omega$. An interconnexion between the topological properties of $G$ and $\Omega$ appears. Further, in order to exhibit in a natural way holomorphic functions with wild boundary behaviour on planar domains, we study a certain type of universality for sequences of continuous mappings from a union of Jordan curves to a domain.

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Stéphane Charpentier, Augustin Mouze. 2021-11-09. Universal sequences of composition operators. https://arxiv.org/abs/2111.05165

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