On the set of hypercyclic vectors for the differentiation operator
Functional Analysis
2012-09-06 v1
Abstract
Let be the differentiation operator acting on the Fr\'echet space \H of all entire functions in one variable with the standard (compact-open) topology. It is known since 1950's that the set of hypercyclic vectors for the operator is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sep\'ulveda whether the set contains (up to the zero function) a non-trivial subalgebra of \H or an infinite dimensional closed linear subspace of \H. In the present article both questions are answered affirmatively.
Cite
@article{arxiv.1209.0984,
title = {On the set of hypercyclic vectors for the differentiation operator},
author = {Stanislav Shkarin},
journal= {arXiv preprint arXiv:1209.0984},
year = {2012}
}