| Dirichlet Shift of Finite Multiplicity |
| Received:June 09, 2010 Revised:April 18, 2011 |
| Key Words:
Dirichlet space Dirichlet shift multiplication operator unitary equivalence.
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| Fund Project:Supported by Tianyuan Foundation of China (Grant No.10926143), Young Science Foundation of Shanxi Province (Grant No.2010021002-2), the National Natural Science Foundation of China (Grant No.10971195) and the Natural Science Foundation of Zhejiang Provinc |
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| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.05.013 |
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