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On analytic structure of weighted shifts on generalized directed semi-trees
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2022-04-20 , DOI: 10.1080/03081087.2022.2065233
Gargi Ghosh 1 , Somnath Hazra 2
Affiliation  

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 H2(β) of formal power series. Under certain conditions, H2(β) turns out to be a reproducing kernel Hilbert space consisting of holomorphic functions on some domain in Cn and the n-tuple of multiplication operators on H2(β) 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.



中文翻译:

关于广义有向半树加权移位的解析结构

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H2个(β)的正式幂级数。在某些条件下,H2个(β)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Cn和乘法运算符的n元组H2个(β)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。

更新日期:2022-04-20
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