正规族与分担函数  

Normal Families and Shared Functions

作　　者：刘晓毅[1] 程春暖[2] 

机构地区：[1]常熟理工学院数学与统计学院,常熟215500 [2]南京师范大学数学科学学院,南京210046

出　　处：《数学学报（中文版）》2013年第6期941-950,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11171045)

摘　　要：设a(≠0)和b(■0)是区域D上的两个全纯函数,并且在函数b的零点处a'不取0.■={f}是区域D内的一族亚纯函数,若每个f的零点都是重级的,且满足f=af'=b,则■在区域D内正规.举例说明结论成立的条件是必不可少的.Let a and b be holomorphic functions on a plane domain D such that a has no zero, b is not zero identically, and at does not take the value 0 at the zeros of b. Let ξ = {f} be a family of meromorphic functions on D, all of whose zeros are multiple, such that f = a→←fl = b. Then the family is normal on D. Examples are given to show the necessity of the conditions.

关 键 词：亚纯函数 正规族 分担值 分担函数 

分 类 号：O174.52[理学—数学]