华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (3): 21-25.

• 数学 统计学 • 上一篇    下一篇

全纯函数的一个正规族(英)

王晓晶1,2; 庞学诚2

  

  1. 1. 淮阴师范学院 数学系, 江苏 淮安 223300; 2. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2004-04-19 修回日期:2004-12-13 出版日期:2006-05-25 发布日期:2006-05-25
  • 通讯作者: 王晓晶

Normal Family of Holomorphic Functions(English)

WANG Xiao-jing1,2, PANG Xue-cheng2   

  1. 1. Department of Mathematics, Huaiyin Teachers'College, Huai'an Jiangsu 223300, China; 2.Department of Mathematics, East China Normal University,Shanghai 200062, China
  • Received:2004-04-19 Revised:2004-12-13 Online:2006-05-25 Published:2006-05-25
  • Contact: WANG Xiao-jing

摘要： 设F为单位圆盘⊿上的 一个全纯函数族，M,N为两个正实数. 如果对于任意的 f∈F,f的零点重级≧ m$, 且f(z)=0=> |f(m)(z)| ≦M , f(m)(z)=1 => |f(z)| ≧N则F在⊿上正规.

关键词: 正规族, 整函数, 全纯函数, 正规族, 整函数, 全纯函数

Abstract: A normality criterion for a family of holomorphic functions was got. Let F be a family of holomorphic functions on the unit disk ⊿, all of whose zeros are of multiplicity at least m; let M,N be two positive numbers; if for any f∈F, f(z)=0
=> |f(m)(z)| ≦M ,f(m)(z)=1 => |f(z)| ≧N , then F is normal on ⊿.

Key words: entire function, holomorphic function, normal family, entire function, holomorphic function

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