关于Ошкин的一个定理  

On the Theorem of Ошкин

作　　者：方明亮[1] 徐万松[2] 

机构地区：[1]南京师范大学数学系,南京210024 [2]南京航空航天大学数理力学系,南京210016

出　　处：《南京航空航天大学学报》1993年第5期714-718,共5页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：本文研究了全纯函数族的正规性,得到如下结果: 定理1 设为区域D上的一族全纯函数,n,k(k≥2)为两正整数,占为非零有穷复数,a_1(z),a_2(z),…,a_k(z)均在D内全纯。若对中每一个函数f(z)均有:(1)f(z)的零点重数≥k;(2)f^n(z){f^((k))(z)+a_1(z)f^((k-1))(z)+…a_k(z)f(z)}≠b,则在D正规。In this paper the normality of a family of holomorphic functions is studied and the following result is obtained:Theorem 1 Suppose is a family of holomorphic function in a domain D.n,k(≥2) are positive integers, b≠ 0 is a finite complex number, a1(z) ,a2(z) , … ,ak(z) are holomorphic functions in D . If for every f(z) in 3,(1) the order of zeros of f(z) ≥ k ;(2)fn(z){f(k)U) +a1(2)f(k-1))(2) + … +ak(z)/(z)}≠b. Then is normal in D .

关 键 词：复分析 全纯函数 半纯函数 正规族 

分 类 号：O174.52[理学—数学]