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

摘要

We generalize a result for the translation C-0-semigroup on L-p(R+, mu) about the equivalence of being chaotic and satisfying the Frequent Hypercyclicity Criterion due to Mangino and Peris [8] to certain weighted composition C-0-semigroups. Such C-0-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 C-0-semigroups on Sobolev spaces are also considered. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim