论文标题
广义向后移动运算符和有理功能的不变子空间
Invariant subspaces of a generalized backward shift operator and rational functions
论文作者
论文摘要
我们在所有Holomorthic函数的Frechet空间中，在复杂平面的简单连接域$ω$上，在所有Holomorthic函数的Frechet空间中获得了通用的向后移动操作员（Pommiez Operator）的完整表征。在定义该运算符的函数的情况下，没有$ω$中的零，所有此类子空间都是有限的。如果另外$ω$与复杂平面一致，则考虑的操作员是单细胞的。如果此功能在$ω$中具有零，则提到的不变子空间的家族分为两个类别：第一个组成是有限维子空间，第二个是Infinite二维子空间。
We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $Ω$ of the complex plane, containing the origin. In the case when the function, which defines this operator, is not has zeros in $Ω$ all such subspaces are finite-dimensional. If additionally $Ω$ coincides with the complex plane, then the considered operator is unicellular. If this function has zeros in $Ω$, then the family of mentioned invariant subspaces splits into two classes: the first consists of finite-dimensional subspaces, and the second of infinite-dimensional ones.
