| 分担集合的亚纯函数正规族 |
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| 引用本文： | 刘晓毅,常建明. 分担集合的亚纯函数正规族[J]. 数学学报, 2011, 0(6): 1049-1056 |
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| 作者姓名： | 刘晓毅 常建明 |
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| 作者单位： | 常熟理工学院数学与统计学院; |
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| 基金项目： | 国家自然科学基金资助项目(10871094) |
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| 摘 要： | 对复平面C的非空有限子集S_1和S_2,记在复平面区域D内满足{z∈D:f(z)∈S_1}={z∈D:f′(z)∈S_2}的全体亚纯函数f形成的函数族为D,那么当S_1和S_2共有至少12个元素对函数族D正规.特别地,当S_1具有至少三个复数时,我们得到了准确的结果.
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| 关 键 词： | 亚纯函数 正规族 分担集合 |
Normal Families of Meromorphic Functions and Shared Sets |
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| Xiao Yi LIU Jian Ming CHANG School of Mathematics , Statistics,Changshu Institute of Technology,Changshu ,P.R.China. Normal Families of Meromorphic Functions and Shared Sets[J]. Acta Mathematica Sinica, 2011, 0(6): 1049-1056 |
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| Authors: | Xiao Yi LIU Jian Ming CHANG School of Mathematics Statistics Changshu Institute of Technology Changshu P.R.China |
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| Affiliation: | Xiao Yi LIU Jian Ming CHANG School of Mathematics and Statistics,Changshu Institute of Technology,Changshu 215500,P.R.China |
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| Abstract: | For nonempty finite sets S1 and S2 and a domain D on C,denote by 1,S2>D the family of meromorphic functions f which satisfy {z∈D:f（z）∈S1} = {z∈D:f’（z）∈S2}.We prove that if S1 and S2 have totally at least 12 elements, then 1,S2>D is normal.In particular,when S1 has at least three elements,we get the sharp results. |
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| Keywords: | meromorphic functions normal family shared sets |
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