关于全纯函数的正规定则

Normal Criteria of Holomorphic Unctions

研究涉及微分多项式与公共值的全纯函数族的正规性问题.设F为区域D内的全纯函数族,n 1为任一正整数,b为有限常数,如果对F中任意两个函数f与g,fn(f-1)f′与gn(g-1)g′在D内都以b为公共值,则F在D内正规.此结果对亚纯函数不成立.

In this paper we study the problem of normal families of holomorphic functions concerning differiantal polynomials and shared values and prove that a family F of holomorphic functions in a domain D is normal if for each pair of functions fand g in f^n（f-1）f′and g^n（g-1）g′ share a finite value b in D where n ≥ 1 is a positive integer. This result is not true for meromorphic functions.