关于加权复合半群的频繁超循环性准则的一个注记及其在线性von Foerster-Lasota方程中的应用
A remark on the frequent hypercyclicity criterion for weighted composition semigroups and an application to the linear von Foerster-Lasota equation
摘要：
本文将$L^p(\R_+,μ)$上的平移$C_0$ -半群的一个结果推广到某些加权复合$C_0$ -半群上，证明了该结果是混沌的且满足Mangino和Peris的频繁超循环准则.当处理一阶线性偏微分算子的初值问题时，这样的$C_0$ -半群以一种自然的方式出现.我们将我们的结果应用到数学生物学中的线性冯福斯特-Lasota方程。还研究了索伯列夫空间上的加权复合$C_0$ -半群.
英文摘要：
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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