Miranda正规定则的推广

The Generalization of Miranda's Normality Criterion

设F为单位圆盘上的一个全纯函数族,a,b,c为三个有穷复数,满足b≠0,b≠a,c≠0,若对任意f∈F,f的零点重级至少为k,且f=0时f(k)=a,f(k)=b时f=c,则F在单位圆盘上正规.推广了Miranda正规定则.

In this paper we generalize Miranda＇s normality criterion and obtain the following result. Let F be a family of holomorphic functions on the unit disc△, all of whose zeros are of multiplicity at leastk. Let a, b, c be three finite complex numbers satisfying b≠0, b ≠ a, c ≠0.If for any f∈ F, f^（k） = a whenever f = 0, f = cwhenever f^（k） = b ,then F is normal on △.