论文标题
积极的不可还原的半群及其长期行为
Positive irreducible semigroups and their long-time behaviour
论文作者
论文摘要
概念\ emph {perron-frobenius理论}通常是指操作员半群的三个属性之间的相互作用：阳性，频谱和长期行为。这些相互作用带来了一个深刻的理论，并具有大量应用。 通过简要介绍该领域和许多示例，我们强调了该主题的两个方面，这两者都与半群的长期行为有关：（i）经典问题如何使用半群的积极性来证明与均值为$ t \ to \ infty $的平衡。 （ii）较新的现象本身有时仅出于大$ t $而发生，而在较小的时间则没有。
The notion \emph{Perron-Frobenius theory} usually refers to the interaction between three properties of operator semigroups: positivity, spectrum and long-time behaviour. These interactions gives rise to a profound theory with plenty of applications. By a brief walk-through of the field and with many examples, we highlight two aspects of the subject, both related to the long-time behaviour of semigroups: (i) The classical question how positivity of a semigroup can be used to prove convergence to an equilibrium as $t \to \infty$. (ii) The more recent phenomenon that positivity itself sometimes occurs only for large $t$, while being absent for smaller times.
