A quantitative interpretation of the frequent hypercyclicity criterion
Functional Analysis
2019-02-27 v2
Abstract
We give a quantitative interpretation of the Frequent Hypercyclicity Criterion. Actually we show that an operator which satisfies the Frequent Hypercyclicity Criterion is necessarily A-frequently hypercyclic, where A refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the "frequency" measured by the Frequent Hypercyclicity Criterion. Moreover we construct an example of unilateral weighted shift which is frequently hypercyclic but not A-frequently hypercyclic on a particular scale.
Keywords
Cite
@article{arxiv.1611.04368,
title = {A quantitative interpretation of the frequent hypercyclicity criterion},
author = {Romuald Ernst and A Mouze},
journal= {arXiv preprint arXiv:1611.04368},
year = {2019}
}