What question did this study set out to answer?

This research aims to establish a criterion for identifying frequent hypercyclicity in convolution operators applied to entire functions.

June 3, 2026Open Access

Frequently Hypercyclic Sequences of Differential Operators on the Space of Entire Functions

Key Points

This research aims to establish a criterion for identifying frequent hypercyclicity in convolution operators applied to entire functions.
Developed a criterion based on the non-vanishing of generating functions on a specified closed annulus.
Analyzed the relationship between the modulus of terms in the sequence and surrounding terms.
Confirmed that the condition for generating functions leads to frequent hypercyclicity in the operator sequences.
Demonstrated that sequential control of moduli significantly supports hypercyclic behavior.

Abstract

Abstract A criterion to obtain frequent hypercyclicity for a sequence of convolution operators on the space of entire functions on the complex plane is provided. The criterion involves that the generating functions of the operators do not vanish on an appropriate closed annulus, in the boundary of which the modulus of each term of the sequence is in some sense controlled by the preceding ones or the following ones.

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Discussion

Journals

Results in Mathematics

Institutions

Universidad de Sevilla

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