Frequently hypercyclic translation semigroups

TL;DR

This paper investigates the conditions under which translation semigroups exhibit frequent hypercyclicity on weighted function spaces, establishing analogies with weighted pseudo-shifts and characterizing these properties in various spaces.

Contribution

It introduces a novel characterization of frequent hypercyclicity for translation semigroups via analogies with weighted pseudo-shifts and extends results to weighted L^p-spaces.

Findings

Characterization of frequent hypercyclicity for translation semigroups on weighted spaces

Establishment of an analogy between hypercyclicity for translation semigroups and weighted pseudo-shifts

Extension of hypercyclicity results to weighted L^p-spaces

Abstract

Frequent hypercyclicity for translation $C_0$-semigroups on weighted spaces of continuous functions is investigated. The results are achieved by establishing an analogy between frequent hypercyclicity for the translation semigroup and for weighted pseudo-shifts and by characterizing frequent hypercyclic weighted pseudo-shifts in spaces of vanishing sequences. Frequent hypercylic translation semigroups in weighted $L^p$-spaces are also characterized.