【摘要】 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.更多还原

【Abstract】 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 discΔ,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 Δ.更多还原