杨向东.Hardy-Smirnov空间中复合算子的收敛性[J].数学研究及应用,2011,31(4):742~748
Hardy-Smirnov空间中复合算子的收敛性
Convergence of Composition Operators on Hardy-Smirnov Space
投稿时间:2009-11-20  最后修改时间:2011-01-13
DOI:10.3770/j.issn:1000-341X.2011.04.021
中文关键词:  复合算子  收敛性  Hardy-Smirnov空间.
英文关键词:composition operators  convergence  Hardy-Smirnov space.
基金项目:云南省自然科学基金(Grant No.2009zc013x);云南省教育厅基础科学基金(Grant No.09Y0079).
作者单位
杨向东 昆明理工大学数学系, 云南 昆明 650093 
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中文摘要:
      受 Joel H.Shapiro 和 Wayne Smith's 的工作 (Journal of Functional Analysis 205 (2003) 62-89)所启发,本文考虑了复平面上单连通区域上Hardy-Smirnov空间中复合算子的收敛性.我们还考虑了单个复合算子之迭代的收敛性.我们工作的意义在于本文的工作不可能通过简单的共形映射而由单位圆的相关结论得到.
英文摘要:
      We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also considered. Our approach is a method from Joel H. Shapiro and Wayne Smith's celebrated work (Journal of Functional Analysis 205 (2003) 62-89). The resulting space is usually not the one obtained from the classical Hardy space of the unit disc by conformal mapping.
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