| 全纯函数的分担值与正规族 |
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| 引用本文： | 李江涛,仪洪勋.全纯函数的分担值与正规族[J].高校应用数学学报(英文版),2006,21(3):335-342. |
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| 作者姓名： | 李江涛 仪洪勋 |
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| 作者单位： | [1]Department of Mathematics, Shandong University, Shandong 250100, China [2]Department of Mathematics, Chongqing University, Chongqing 400044, China |
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| 基金项目： | 山东大学校科研和教改项目
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国家自然科学基金 |
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| 摘 要： | Let F be a family of holomorphic functions in a domain D, k be a positive integer, a, b（≠0）, c（≠0） and d be finite complex numbers. If, for each f∈F, all zeros of f-d have multiplicity at least k, f^（k） = a whenever f=0, and f=c whenever f^（k） = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp.
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| 关 键 词： | 晶体函数 常态族 分享价值 有限复形数 数学分析 |
| 收稿时间： | 2005-09-09 |
Normal families and shared values of holomorphic functions |
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| Li Jiangtao,Yi Hongxun.Normal families and shared values of holomorphic functions[J].Applied Mathematics A Journal of Chinese Universities,2006,21(3):335-342. |
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| Authors: | Li Jiangtao Yi Hongxun |
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| Institution: | (1) Department of Mathematics, Shandong University, 250100 Shandong, China;(2) Department of Mathematics, Chongqing University, 400044 Chongqing, China |
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| Abstract: | Let F be a family of holomorphic functions in a domain D, k be a positive integer,a, b(≠ 0), c(≠ 0) and d be finite complex numbers. If, for each f ∈ F, all zeros of f - d have multiplicity at least k, f(κ) = a whenever f = 0, and f = c whenever f(κ) = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp. |
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| Keywords: | holomorphic function normal family shared value |
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