Upper frequent hypercyclicity and related notions

By Antonio Bonilla, K. Grosse-Erdmann. Revista Matemática Complutense, 2016

58 citations recorded by the source corpus.

Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper frequently hypercyclic weighted backward shifts on sequence spaces, which in turn allows us to come up with various counter-examples in linear dynamics that are substantially simpler than those previously obtained in the literature. More generally, we introduce the notion of upper Furstenberg families A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} and show that our main results hold for the corresponding A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document}-hypercyclic operators.

Subfields: Applied Mathematics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/19b0f6408f7ebd16f8b3f463501e86fcd701ae13

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Statistics and Probability

Citations in the corpus

Frequently recurrent operators (2020, methodology): “Note that each of the hypercyclic properties in the corollary have been characterized in terms of the weights, at least if the basis is unconditional, see [28, Theorem 4.8], [13, Theorem 5.1].”
Linear dynamical systems on Hilbert spaces: typical properties and explicit examples (2017, background): “Then, the set UFHC(T ) of all U-frequently hypercyclic vectors for T is comeager in H ([10], see also [15]), whereas the set FHC(T ) of frequently hypercyclic vectors for T is meager ([41], [10]).”