Hypercyclic homogeneous polynomials on $H(\mathbb C)$
Functional Analysis
2017-07-31 v2
Abstract
It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fr\'echet spaces. We show the existence of hypercyclic polynomials on , by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any -space. We prove that the homogeneous polynomial on defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic.
Keywords
Cite
@article{arxiv.1703.04773,
title = {Hypercyclic homogeneous polynomials on $H(\mathbb C)$},
author = {Rodrigo Cardeccia and Santiago Muro},
journal= {arXiv preprint arXiv:1703.04773},
year = {2017}
}