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| 亚纯函数的Valiron亏函数 | |
| 引用本文： | 卢谦,韩润生,顾永兴. 亚纯函数的Valiron亏函数[J]. 数学学报, 2004, 47(4): 735-740. DOI: cnki:ISSN:0583-1431.0.2004-04-014 |
| 作者姓名： | 卢谦 韩润生 顾永兴 |
| 作者单位： | 1. 四川大学数学学院,成都,610044;西南科技大学理学院,绵阳,621010 2. 重庆大学数理学院,重庆,400044 |
| 摘 要： | 对于开平面内有穷级的超越亚纯函数f(z),本文主要讨论其Valiron亏函数问题,得到f(z)的Valiron亏函数的F_δ-集合必为μ-集合的结论,去掉了陈怀惠等对f(z)的极点的要求。最后指出对于无穷级的情形,也有相应的结论。 |
| 关 键 词： | 亚纯函数 亏函数 μ-集合 |
| 文章编号： | 0583-1431(2004)04-0735-06 |
The Deficient Function of Meromorphic Functions |
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| Qian LU College of Mathematical Science,Sichuan University,Chengdu ,P. R.. China College of Sciences,Southwest University of Science and Technology,Mianyang ,P. R. China Email: luqiankuo@hotmail.comRun Sheng HAN Yong Xing GU College of Mathematics and Sciences,Chongqing University,Chongqing ,P. R. China. The Deficient Function of Meromorphic Functions[J]. Acta Mathematica Sinica, 2004, 47(4): 735-740. DOI: cnki:ISSN:0583-1431.0.2004-04-014 | |
| Authors: | Qian LU College of Mathematical Science Sichuan University Chengdu P. R.. China College of Sciences Southwest University of Science Technology Mianyang P. R. China Email: luqiankuo@hotmail.comRun Sheng HAN Yong Xing GU College of Mathematics Sciences Chongqing University Chongqing P. R. China |
| Affiliation: | Qian LU College of Mathematical Science,Sichuan University, Chengdu 610044, P. R.. China College of Sciences, Southwest University of Science and Technology,Mianyang 621010, P. R. China Email: luqiankuo1965@hotmail.comRun Sheng HAN Yong Xing GU College of Mathematics and Sciences, Chongqing University, Chongqing 400044, P. R. China |
| Abstract: | Let f(z) be a function meromorphic on the plane |z|<+∞ with finiteorder. We point out that F_δ-sets of Valiron deficient functions of f(z) must be μ-sets,eliminating the restriction for the pole of f(z) in the Chen's result. Finally we findthat the corresponding conclusion also holds for meromorphic functions with infiniteorder. |
| Keywords: | Meromorphic functions Deficient functions μ-Sets |
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