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arXiv · 1410.7697

A remark on the frequent hypercyclicity criterion for weighted composition semigroups and an application to the linear von Foerster-Lasota equation

Thomas Kalmes
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Abstract

We generalize a result for the translation $C_0$-semigroup on $L^p(\R_+,μ)$ about the equivalence of being chaotic and satisfying the Frequent Hypercyclicity criterion due to Mangino and Peris 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.

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Thomas Kalmes. 2014-10-28. A remark on the frequent hypercyclicity criterion for weighted composition semigroups and an application to the linear von Foerster-Lasota equation. https://doi.org/10.1002/mana.201400410

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