Universal Sequences of Composition Operators

Let G and Ω be two planar domains. We give necessary and sufficient conditions on a sequence ( ϕ n ) of eventually injective holomorphic mappings from G to Ω for the existence of a function f ∈ H ( Ω ) whose orbit under the composition by ( ϕ n ) is dense in H ( G ). This extends a result of the sam...

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 33; no. 7
Main Authors Charpentier, S., Mouze, A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2023
Springer Nature B.V
Springer
Subjects
Abstract Harmonic Analysis
Analytic functions
Composition
Convex and Discrete Geometry
Differential Geometry
Domains
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Composition operators
47B33
Universal sequences of operators
30K15
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Summary:Let G and Ω be two planar domains. We give necessary and sufficient conditions on a sequence ( ϕ n ) of eventually injective holomorphic mappings from G to Ω for the existence of a function f ∈ H ( Ω ) whose orbit under the composition by ( ϕ n ) is dense in H ( G ). This extends a result of the same nature obtained by Grosse-Erdmann and Mortini when G = Ω . An interconnexion between the topological properties of G and Ω 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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01283-0