Hypercyclic Algebras for convolution operators of unimodular constant term

TL;DR

This paper investigates conditions under which convolution operators with unimodular constant term possess hypercyclic algebras, introducing new eigenvalue criteria for dense strongly algebrable sets of hypercyclic vectors.

Contribution

It provides novel eigenvalue criteria for the existence of hypercyclic algebras in convolution operators with unimodular constant term.

Findings

Established new eigenvalue criteria for hypercyclic algebras.

Proved the existence of densely strongly algebrable sets of hypercyclic vectors.

Extended understanding of hypercyclicity in convolution operators.

Abstract

We study the existence of hypercyclic algebras for convolution operators $\Phi(D)$ on the space of entire functions whose symbol $\Phi$ has unimodular constant term. In particular, we provide new eigenvalue criteria for the existence of densely strongly algebrable sets of hypercyclic vectors.