A remark on the Frequent Hypercyclicity Criterion for weighted composition semigroups and an application to the linear von Foerster–Lasota equation

Abstract

We generalize a result for the translation C₀-semigroup on about the equivalence of being chaotic and satisfying the Frequent Hypercyclicity Criterion due to Mangino and Peris 8 to certain weighted composition C₀-semigroups. Such C₀-semigroups appear in a natural way when dealing with initial value problems for linear first order partial differential operators. We apply our result to the linear von Foerster–Lasota equation arising in mathematical biology. Weighted composition C₀-semigroups on Sobolev spaces are also considered.