论文标题
经常经常发生操作员
Frequently recurrent operators
论文作者
论文摘要
最近对Costakis等人进行的调查的动机。关于线性动力学复发的概念，我们研究了线性操作员的各种更强形式的复发形式，尤其是频繁复发的复发形式。我们研究了一种复发性与相应的高度环境概念，功率界限的影响以及复发性和光谱特性之间的相互作用之间的关系。我们尤其获得了$ \ Mathcal {f} $的Ansari-和Léon-Müller-type定理 - 在Furstenberg family $ \ Mathcal {f} $的非常弱的假设下恢复。这使我们可以作为副产品推断出ansari-和léon-müller-type定理，以$ \ mathcal {f} $ - hypercyclicity。
Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We study, among other things, the relationship between a type of recurrence and the corresponding notion of hypercyclicity, the influence of power boundedness, and the interplay between recurrence and spectral properties. We obtain, in particular, Ansari- and Léon-Müller-type theorems for $\mathcal{F}$-recurrence under very weak assumptions on the Furstenberg family $\mathcal{F}$. This allows us, as a by-product, to deduce Ansari- and Léon-Müller-type theorems for $\mathcal{F}$-hypercyclicity.
