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有限重数的Dirichlet移位
引用本文:赵连阔.有限重数的Dirichlet移位[J].数学研究与评论,2011,31(5):874-878.
作者姓名:赵连阔
作者单位:山西师范大学数学与计算机科学学院, 山西 临汾 041004
基金项目:数学天元基金(Grant No.10926143),山西省青年科技基金(Grant No.2010021002-2),国家自然科学基金(Grant No.10971195),浙江省自然科学基金(Grant Nos.Y6090689;Y6110260).
摘    要:In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n + 1 (n ≥ 0) if and only if its symbol is c zn+1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.

关 键 词:Dirichlet  space  Dirichlet  shift  multiplication  operator  unitary  equivalence.
收稿时间:6/9/2010 12:00:00 AM
修稿时间:2011/4/18 0:00:00

Dirichlet Shift of Finite Multiplicity
Lian Kuo ZHAO.Dirichlet Shift of Finite Multiplicity[J].Journal of Mathematical Research and Exposition,2011,31(5):874-878.
Authors:Lian Kuo ZHAO
Institution:School of Mathematics and Computer Science, Shanxi Normal University, Shanxi 041004, P. R. China
Abstract:In this paper, we show that a multiplication operator on the Dirichlet space $\mathcal{D}$ is unitarily equivalent to Dirichlet shift of multiplicity $n+1~(n\geq 0)$ if and only if its symbol is $c\,z^{n+1}$ for some constant $c$. The result is very different from the cases of both the Bergman space and the Hardy space.
Keywords:Dirichlet space  Dirichlet shift  multiplication operator  unitary equivalence  
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