摘要
设k是正整数,F是开平面上的区域D的亚纯函数族,F中每个函数f(z)∈F的零点重数至少为k+1,极点重数至少为3,而a(z)为D上的全纯函数,a(z)不恒等于0。对于F中的每个函数f(z)∈F,若f(z)的全纯系数的线性微分多项式L(f)满足L(f)≠a(z),z∈D,则F在D上正规。
In this paper, we obtain the following normal criterion： Let F be a family of meromorphic functions in domain D, all of whose zeros have multiplicity k ＋ 1 at least and of whose poles have multiplicity 3 at least. If there exists analytic function a（z） on D, such that for every functionf（z）εF, L（f） ≠ a（z）, zεD, then F is normal family on D. Where L（f） is a linea differential polynomial off（z） with holomorphic coefficient aj（z） （j = 1,2,.. ,k - 1 ） and k is some positive number.
出处
《西南科技大学学报》
CAS
2010年第1期89-93,共5页
Journal of Southwest University of Science and Technology
关键词
亚纯函数
微分多项式
正规族
Meromorphic functions, Differential polynomial, Normal criterion
