华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (2): 154-159.

• 数学 • 上一篇    下一篇

与例外函数列相关的正规族

杨 刘， 陈巧玉   

  1. 华东师范大学~~数学系, 上海 200241
  • 收稿日期:2012-04-01 修回日期:2012-07-01 出版日期:2013-03-25 发布日期:2013-03-20

Normal families on sequence of omitted functions

YANG Liu, CHEN Qiao-yu   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2012-04-01 Revised:2012-07-01 Online:2013-03-25 Published:2013-03-20

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摘要： 设~$\{f_{n}\}$~是区域~$D$~内的亚纯函数列,~其零点的重级均~$\geq3$,
且均仅有一个重级极点.
~$\{h_{n}\}$~是~$D$~内的亚纯函数列,~且~$h_{n}\Rightarrow h$~于~$D$,
$h \not \equiv \infty,h \ne 0$. 若~$f'_{n}\ne h_{n}$,
则~$\{f_{n}\}$~在~$D$~内正规.

关键词: 亚纯函数, 正规族, 例外函数列

Abstract: Let~$\{f_{n}\}$~be a sequence  of meromorphic functions on
a domain~$D$,~all of whose zeros have multiplicity at least $ 3$,and
each of which has a multiple pole. Let $\{h_{n}\}$~be a sequence of
meromorphic functions on~$D$, such that~$\{h_{n}\}$~converges
spherically locally uniformly to  a function~$h$ which is
meromorphic and zero-free on $D$. If~$f'_{n}\ne h_{n}$,
then~$\{f_{n}\}$~is normal on~$D$.

Key words: meromorphic function, normal family, sequence of omitted functions

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