华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (3): 6-10.

• 数学 统计学 • 上一篇    下一篇

微分多项式的正规族(英)

王晓晶1,2， 庞学诚2

  

  1. 1. 淮阴师范学院 数学系，淮安 223001； 2. 华东师范大学 数学系，上海 200062
  • 收稿日期:2003-09-03 修回日期:2003-11-10 出版日期:2004-09-25 发布日期:2004-09-25
  • 通讯作者: 王晓晶

Normal Families Concerning Differential Polynomial

WANG Xiao-jing1,2, PANG Xue-cheng2   

  1. 1. Department of Mathematics, Huaiyin Teachers’ College, Huaiyin 223001, China; 2. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2003-09-03 Revised:2003-11-10 Online:2004-09-25 Published:2004-09-25
  • Contact: WANG Xiao-jing

摘要：

给出了一个一般性的正规定则，改进了顾永兴［1］和朱经浩［2］的结果. 设F为区域D上的一个亚纯函数族，h≠0,a0,a1,…,am-1为区域D上的全纯函数。如果对于任意的f∈F，f的零点重级≥m+3并且f(m)(z)+am-1(z)f(m-1)(z)+…+a1(z)f′(z)+a0(z)f(z)≠h(z) z∈D,则F在区域D上正规.

关键词: 正规族, 亚纯函数, 全纯函数, 微分多项式, 正规族, 亚纯函数, 全纯函数, 微分多项式

Abstract: In this paper a general normal criterion is obtained, which improves the results given by Gu YX［1］ and Zhu JH［2］. Let F be a family of meromorphic functions on domain D, all of whose zeros are of multiplicity at least m+3. Let h≠0, a0, a1, …, am-1 be holomorphic functions on D. If for any f∈F, L(f)(z)=f(m)(z)+am-1(z)f(m-1)(z)+…+a1(z)f′(z)+a0(z)f(z)≠h(z), z∈D, then F is normal on D.

Key words: meromorphic functions, holomorphic functions, differential polynomial, normal family, meromorphic functions, holomorphic functions, differential polynomial

中图分类号: