Subspaces of frequently hypercyclic functions for sequences of composition operators
Luis Bernal-Gonz\'alez, M. Carmen Calder\'on-Moreno, Andreas Jung and, Jos\'e A. Prado Bassas
TL;DR
This paper establishes a new criterion for when sequences of composition operators on holomorphic functions are frequently hypercyclic, enabling the construction of large subspaces of such functions.
Contribution
It introduces an improved criterion for frequent hypercyclicity of composition operators, applicable to dense and large closed subspaces of functions.
Findings
New criterion for frequent hypercyclicity of composition operators
Existence of dense subspaces of frequently hypercyclic functions
Large closed subspaces of functions with frequent hypercyclicity
Abstract
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such criterion improves some already known special cases and, in addition, it is also valid to provide dense vector subspaces as well as large closed ones consisting entirely, except for zero, of functions that are frequently hypercyclic.
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