Dirichlet Shift of Finite Multiplicity  

作　　者：Lian Kuo ZHAO 

机构地区：[1]School of Mathematics and Computer Science, Shanxi Normal University, Shanxi 041004, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第5期874-878,共5页数学研究与评论（英文版）

基　　金：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);the Natural Science Foundation of Zhejiang Province (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.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. 

分 类 号：O177.1[理学—数学]