论文标题
树的离散功能空间上的分化操作员
The differentiation operator on discrete function spaces of a tree
论文作者
论文摘要
在本文中，我们研究了作用于离散功能空间的分化操作员。这是在无限生根树上定义的功能空间。我们通过与组成操作员的联系讨论了该操作员的界限和紧凑性。此外，我们讨论了操作员的规范和频谱，并考虑何时可以使用等轴测图。然后，我们将这些结果应用于作用于离散Lipschitz空间和加权Banach空间的操作员，以及在同质树上定义的耐寒空间。
In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined on an infinite rooted tree. We discuss, through its connection with composition operators, the boundedness and compactness of this operator. In addition, we discuss the operator norm and spectrum, and consider when such an operator can be an isometry. We then apply these results to the operator acting on the discrete Lipschitz space and weighted Banach spaces, as well as the Hardy spaces defined on homogeneous trees.
