摘要
对于单位园D={|Z|<1}内的全纯函数族F,有一个熟知的Miranda定则:若对任一f∈F都有:f(z)≠0,f^(k)(z)≠1(k为某一正整数),则F在D内是正规的。本文旨在引进广义Borel例外值等概念,给出相应的更普遍的正规定则。定义:设f(z)是D={|z|<1}内的全纯函数,a为一复数,若:
The author proves in this paper the following
Theorem. Suppose that F is a family of holomorphic functions in {|z|<1} and M is a posi-
tive number. If for any f∈F, f(z)≠0 and f^(k)(z) assumes 1 as a pseudo-Borel exceptional
value with the exponent<M. Then F is normal.
出处
《纯粹数学与应用数学》
CSCD
1990年第1期87-89,共3页
Pure and Applied Mathematics
