不取零点的亚纯函数族的正规性

数学季刊 ›› 2013, Vol. 28 ›› Issue (3): 402-407.

不取零点的亚纯函数族的正规性

Department of Applied Mathematics, South China Agricultural University

收稿日期:2012-04-27 出版日期:2013-09-30 发布日期:2023-02-24
作者简介:LIU Dan(1978-), female, native of Wuhan, Hubei, a lecturer of South China Agricultural University, M.S.D., engages in the theory of complex analysis; DENG Bing-mao(1986-), male, native of Jieyang, Guangdong, a lecturer of South China Institute of Software Engineering of Guangzhou University, M.S.D, engages in the theory of complex analysis; YANG De-gui(1967-), male, native of Hefei, Anhui, a professor of South China Agricultural University, Ph.D., engages in the theory of complex analysis.
基金资助:
Supported by the NNSF of China(11371149)

Normal Families of Zero-free Meromorphic Functions

Department of Applied Mathematics, South China Agricultural University

Received:2012-04-27 Online:2013-09-30 Published:2023-02-24
About author:LIU Dan(1978-), female, native of Wuhan, Hubei, a lecturer of South China Agricultural University, M.S.D., engages in the theory of complex analysis; DENG Bing-mao(1986-), male, native of Jieyang, Guangdong, a lecturer of South China Institute of Software Engineering of Guangzhou University, M.S.D, engages in the theory of complex analysis; YANG De-gui(1967-), male, native of Hefei, Anhui, a professor of South China Agricultural University, Ph.D., engages in the theory of complex analysis.
Supported by:
Supported by the NNSF of China(11371149)

摘要/Abstract

摘要： Let F be a family of zero-free meromorphic functions in a domain D, let h(z)≡0 be a holomorphic function in D and let k be a positive integer.If,for each f∈F, P(f)(z)-h(z) has at most k distinct zeros(ignoring multiplicity)in D, where P(f)=f(k)(z)+a1(z)f(k-1)(z)+···+ak(z)f(z) is a diferential polynomial of f and aj(z)(j=1,2,···,k) are holomorphic functions in D, then F is normal in D. This extends the results due to Deng[2], Chang[1], Gu[3], Yang[12], etc.

关键词: meromorphic function, normality, zero-free

Abstract: Let F be a family of zero-free meromorphic functions in a domain D, let h(z)≡0 be a holomorphic function in D and let k be a positive integer. If, for each f∈F, P(f)(z)-h(z) has at most k distinct zeros(ignoring multiplicity)in D, where P(f)=f(k)(z)+a1(z)f(k-1)(z)+···+ak(z)f(z) is a diferential polynomial of f and aj(z)(j=1,2,···,k) are holomorphic functions in D, then F is normal in D. This extends the results due to Deng[2], Chang[1], Gu[3], Yang[12], etc.

Key words: meromorphic function, normality, zero-free

中图分类号:

O174.5

刘丹, 邓炳茂, 杨德贵. 不取零点的亚纯函数族的正规性[J]. 数学季刊, 2013, 28(3): 402-407.

LIU Dan, DENG Bing-mao, YANG De-gui. Normal Families of Zero-free Meromorphic Functions[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(3): 402-407.

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