论文标题
在两个通勤运算符下减少和不变子空间
Reducing and Invariant subspaces under two commuting shift operators
论文作者
论文摘要
在本文中，我们表征了单位圆中定义的平方集成函数空间的减少和不变子空间，并且具有多重性的某些耐寒空间中的值。 我们考虑减少双侧移位的子空间，同时在当地的单侧偏移下是不变的。我们还研究减少两个运营商的子空间。获得的条件是Helson和Beurling Lax-Halmos定理中关于双侧和单侧移位不变性的类型。我们研究的动机受到了有关移动不变空间中动态采样的最新结果的启发。
In this article, we characterize reducing and invariant subspaces of the space of square integrable functions defined in the unit circle and having values in some Hardy space with multiplicity. We consider subspaces that reduce the bilateral shift and at the same time are invariant under the unilateral shift acting locally. We also study subspaces that reduce both operators. The conditions obtained are of the type of the ones in Helson and Beurling-Lax-Halmos theorems on characterizations of the invariance for the bilateral and unilateral shift. The motivations for our study were inspired by recent results on Dynamical Sampling in shift-invariant spaces.
