| 多连通区域单叶函数 |
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| 引用本文： | 杨维奇.多连通区域单叶函数[J].北京理工大学学报(英文版),1994,3(2):99-113. |
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| 作者姓名： | 杨维奇 |
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| 作者单位： | 北京理工大学应用数学系 |
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| 基金项目： | 高等学校博士学科专项科研基金 |
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| 摘 要： | 本文是作者在多连通区域单叶函数领域研究成果的总结．文中给出：Ｖｉｌｌａｔ公式的两个极简单证明；多连通区域的Ｓｃｈｗａｒｚ公式，Ｐｏｉｓｓｏｎ公式，Ｐｏｉｓｓｏ－Ｊｅｎｓｅｎ公式；多连通区域解析函数一参族对参数的可微性定理；多连通区域单叶函数的变分定理和参数表示定理；一类泛函极值问题的解．
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| 关 键 词： | 单叶函数 积分表示 变分法／多连通区域 参数表示法 极值问题 |
On Univalent Functions in Multiply Connected Domains |
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| Yan Weiqi.On Univalent Functions in Multiply Connected Domains[J].Journal of Beijing Institute of Technology,1994,3(2):99-113. |
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| Authors: | Yan Weiqi |
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| Affiliation: | Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081 |
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| Abstract: | The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals. |
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| Keywords: | univalent functions integral representation variational methods/multiply connected domains parametric representation method extremal problem |
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