Common hypercyclic functions for translation operators with large gaps

TL;DR

This paper proves the existence of entire functions that are hypercyclic for a wide range of translation operators with large gaps, expanding understanding of operator dynamics in complex analysis.

Contribution

It establishes the existence of common hypercyclic functions for uncountable families of translation operators with large gaps, a novel result in operator theory.

Findings

Existence of common hypercyclic functions for large-gap translation operators

Extension to uncountable families of operators

Advances understanding of hypercyclicity in complex analysis

Abstract

We prove the existence of common hypercyclic, entire functions for certain uncountable families of traslation type operators with relative large gaps.