Year: 2012
Type: preprint
Abstract: Let $D$ be the differentiation operator $Df=f'$ acting on the Fréchet space $\H$ of all entire functions in one variable with the standard (compact-open) topology. It is known since 1950's that the set $H(D)$ of hypercyclic vectors for the operator $D$ is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the set $H(D)$ 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.
Source: arXiv (Cornell University)
Author: Shkarin, Stanislav
Institution: Queen's University Belfast
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2964196303