Inspired by natural classes of examples, we define generalized directed semi-trees and construct weighted shifts on them. Given an n-tuple of generalized directed semi-trees with certain properties, we associate an n-tuple of multiplication operators on a Hilbert space ${\mathcal{H}}^2(\beta )$ of formal power series. Under certain conditions, ${\mathcal{H}}^2(\beta )$ turns out to be a reproducing kernel Hilbert space consisting of holomorphic functions on some domain in ${\mathbb{C}}^n$ and the n-tuple of multiplication operators on ${\mathcal{H}}^2(\beta )$ is unitarily equivalent to an n-tuple of weighted shifts on generalized directed semi-trees. Finally, we exhibit two classes of examples of n-tuples of operators, which can be intrinsically identified as weighted shifts on generalized directed semi-trees.

受自然类示例的启发，我们定义了广义有向半树并在其上构造加权移位。给定具有某些属性的广义有向半树的n元组，我们将乘法运算符的n元组关联到希尔伯特空间${\mathcal{H}}^{\mathrm{2个}}(\beta )$的正式幂级数。在某些条件下，${\mathcal{H}}^{\mathrm{2个}}(\beta )$结果证明是一个再生核 Hilbert 空间，由在某个域上的全纯函数组成${\mathbb{C}}^n$和乘法运算符的n元组${\mathcal{H}}^{\mathrm{2个}}(\beta )$统一等价于广义有向半树上的加权移位的n元组。最后，我们展示了两类n元组运算符的例子，它们本质上可以被识别为广义有向半树上的加权移位。