| 连通区域的Dirichlet空间上的复合算子 |
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| 引用本文： | 夏锦,王晓峰.连通区域的Dirichlet空间上的复合算子[J].广州大学学报(自然科学版),2008,7(2):18-21. |
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| 作者姓名： | 夏锦 王晓峰 |
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| 作者单位： | 广州大学,数学与信息科学学院,广东,广州,510006 |
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| 摘 要： | 讨论了从复平面上一个多连通区域的Dirichlet空间到另一个多连通区域的Dirichlet空间的复合算子为可逆与Fredholm算子的条件,得到的结论是从复平面上一个多连通区域的Dirichlet空间到另一个多连通区域的Dirichlet空间的复合算子可逆当且仅当它的诱导映射是单射同时诱导映射的值域满足某种边界条件;从复平面上一个多连通区域的Dirichlet空间到另一个多连通区域的Dirichlet空间的复合算子是Fredholm算子当且仅当它的诱导映射是单射同时它的值域满足某种边界条件.
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| 关 键 词： | 连通区域 复合算子 Fredholm复合算子 connected domain composition operator Fredholm composition operator |
| 文章编号： | 1671-4229(2008)02-0018-04 |
| 修稿时间： | 2007年3月23日 |
Composition operators of Dirichlet spaces on connected domains |
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| XIA Jin,WANG Xiao-feng.Composition operators of Dirichlet spaces on connected domains[J].Journal og Guangzhou University:Natural Science Edition,2008,7(2):18-21. |
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| Authors: | XIA Jin WANG Xiao-feng |
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| Abstract: | In this paper,the authors discuss how a composition operator from one Dirichlet space on connected domains in complex plane to another Dirichlet space on connected domains in complex plane be invertible or Fredholm operator.The authors attain the results that the composition operator is invertible if and only if the inducing mapping of the composition operator is an injective,and the range of the inducing mapping satisfies some kind of boundary condition.Moreover,the composition operator is Fredholm operator if and only if the inducing mapping of the composition operator is an injective,and the range of the inducing mapping satisfies some kind of boundary condition. |
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| Keywords: | connected domain composition operator Fredholm composition operator |
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