Common hypercyclic vectors for families of backward shift operators

TL;DR

This paper establishes conditions for the existence of common hypercyclic vectors for families of backward shift operators, generalizing previous results and applying to a broad class of hypercyclic operators.

Contribution

It provides necessary and sufficient conditions for common hypercyclic vectors for multiples of backward shift operators along sparse powers, extending prior work to a more general setting.

Findings

Conditions for common hypercyclic vectors are characterized.

Results apply to a wide class of hypercyclic operators.

Generalizes previous results on the full orbit of the backward shift.

Abstract

We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the full orbit of the backward shift. Some of our results are valid in a more general context, in the sense that they apply for a wide class of hypercyclic operators.