李三华,吴高翔
涉及例外函数的亚纯函数族
*李三华,吴高翔
(井冈山大学数理学院,江西,吉安 343009)
通过研究涉及例外函数的亚纯函数族,推广了由Montel建立的一个正规定则,进而得到了相应亚纯函数族的正规定则。由此把例外值推广至例外函数的情形。
亚纯函数;例外函数;正规族
Montel首先把函数族的正规性与函数的取值问题联系起来,得到了经典的Montel定则[1]。
庞学诚和L.zalcman[2]对Montel定则做过一定的研究。如今我们将Montel定则由例外值推广至例外函数的情形,得到如下结果:
[1] Montel P. Lecons sur familles mormales ed fonctions analytiques et leurs applications[M]. Gauthier-Villars, Pares,1927.
[2] Pang Xuecheng, Zalcman L. Normal families of meromorphic functions with multiple zeros and poles [J]. Israel J,Math, 2003, 136: 1-9.
[3] Gu Yongxing, Pang Xuecheng Fang Mingliang. The theory of normal family and its application[M]. Beijing:Science Press, 2002, 24.
[4] Schiff J. Normal families [M]. New York:Springer, 1993: 75-76.
[5] Pang Xuecheng, Zalcman L. Normal families and shared values [J]. Bull London Math Soc, 2000, 32: 325-331.
[6] 顾永兴,庞学诚,方明亮. 正规族理论及其应用 [M]. 北京: 科学出版社, 2007.
NORMAL FAMILIES OF MEROMORPHIC FUNCTION ASSOCIATED WITH OMITTED FUNCTIONS
*LI San-hua,WU Gao-xiang
(School of Mathematics and Physics, Jinggangshan University, Ji’an, Jiangxi 343009, China)
We study the family of meromorphic functions related to omitted functions and the promotion of a normal criteria established by Montel. Furthermore, we obtain the corresponding normal criterion of meromorphic functions, which can promote the omitted values to omitted functions situation.
meromorphic function; omitted function; normality
1674-8085(2014)01-0008-03
O174.52
A
10.3969/j.issn.1674-8085.2014.01.002
2013-09-24;
2013-10-26
吉安市科技计划项目(吉市科计字[2012]32号9)
*李三华(1982-),女,江西吉安人,讲师,硕士,主要从事复分析研究(E-mail: lisanhua@sina.com);
吴高翔(1980-),男,江西吉安人,讲师,主要从事微分方程研究(E-mail: wugaoxiang_jgsu@163.com).