| 侯绳照,卫淑云,毋丽丽,赵连阔.Dirichlet空间中的正交函数[J].数学年刊A辑,2020,41(1):069~76 |
| Dirichlet空间中的正交函数 |
| Orthogonal Functions in the Dirichlet Space |
| Received:March 29, 2018 Revised:January 08, 2019 |
| DOI：10.16205/j.cnki.cama.2020.0005 |
| 中文关键词: Dirichlet space, Orthogonal function, Counting function, Induced measure |
| 英文关键词:Dirichlet space, Orthogonal function, Counting function, Induced measure |
| 基金项目:本文受到国家自然科学基金(No.11571248,No.11171245,No.11771401)的资助. |
| Author Name | Affiliation | E-mail | | HOU Shengzhao | School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China. | shou@suda.edu.cn | | WEI Shuyun | School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China. | swei@suda.edu.cn | | WU Lili | School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China. | 2857145055@qq.com | | ZHAO Liankuo | Corresponding author. School of Mathematics and Computer Science, Shanxi Normal University,Linfen 041004, Shanxi, China. | liankuozhao@sina.com |
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| 中文摘要: |
| 主要考虑了Dirichlet空间中的正交函数. 主要结论表明单位圆盘中的一个解析自映射是Dirichlet空间中的正交函数,
当且仅当其所对应的计数函数是本质径向的; 当且仅当其所对应的诱导测度是径向的. 作为主要结论的一个应用,
给出了单位圆盘上的单叶解析函数和闭单位圆盘上的解析函数是Dirichlet空间中正交函数的完全刻画. |
| 英文摘要: |
| This paper focuses on orthogonal functions in the
Dirichlet space. The authors show that an analytic self-map of the unit disk is orthogonal in the Dirichlet space if and only if the corresponding counting function is essential radial, and if and only if the corresponding induced measure is radial. As an application, the authors completely characterize orthogonal functions analytic in a neighborhood of the closed unit disk or univalent in the unit disk. |
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