全纯函数的正规族

吕锋, 徐俊峰, 仪洪勋

数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 963-974.

PDF(468 KB)
PDF(468 KB)
数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 963-974. DOI: 10.12386/A2010sxxb0107
论文

全纯函数的正规族

    吕锋1, 徐俊峰2, 仪洪勋3
作者信息 +

Normal Families of Holomorphic Functions

    Feng Lü1, Jun Feng XU2, Hong Xun YI3
Author information +
文章历史 +

摘要

本文证明了两个正规族定理,分别改进了张国明、孙伟和庞学诚的一个结果和徐焱的一个结果.

 

Abstract

In this paper, we prove two theorems of normal family which greatly improve a results of G. Zhang, W. Sun, X. Pang and a result of Y. Xu, respectively.

 

关键词

整函数 / 全纯函数 / 正规族

Key words

entire functions / holomorphic functions / normal family

引用本文

导出引用
吕锋, 徐俊峰, 仪洪勋. 全纯函数的正规族. 数学学报, 2010, 53(5): 963-974 https://doi.org/10.12386/A2010sxxb0107
Feng Lü, Jun Feng XU, Hong Xun YI. Normal Families of Holomorphic Functions. Acta Mathematica Sinica, Chinese Series, 2010, 53(5): 963-974 https://doi.org/10.12386/A2010sxxb0107

参考文献


[1] Schiff J., Normal Families, New York: Springer, 1993.

[2] Yang C. C., Yi H. X., The Uniqueness Theory of Meromorphic Functions, Beijing: Science Press, 2003.

[3] Pang X. C., Fang M. L., Zalcman L., Normal families of holomorphic functions with multiple zeros, Conform. Geom. Dyn., 2007, 11: 101--106.

[4] Zhang G. M., Sun W., Pang X. C., On the normality of certain kind holomorphic functions, Chinese Annals of Mathematics, Series A., 2005, 26: 765--770.

[5] Wang J. P., Entire functions that share a polynomial with their derivatives, J. Math. Anal. Appl., 2006, 320(2): 703--717.

[6] Bergweiler W., Bloch's principle, Comput. Methods Funct. Theory., 2006, 6: 77--108.

[7] Xu Y., Share fix-points and normal families, Arch. Math., 2005, 84: 512--518.

[8] Nevo S., Pang X. C., Zalcman L., Quasinormality and meromorphic functions with multiple zeros, Journal d'Analyse Math\'ematique, 2007, 101: 1--24.

[9] Pang X. C., Yang D. G., Zalcman L., Normal families and omitted functions, Indiana Univ. Math. J., 2005, 54: 223--235.

[10] Clunie J., Hayman W. K., The spherical derivative of integral and meromorphic functions, Comment. Math. Helv., 1966, 40: 117--148.

[11] Pang X. C., Zalcman L., Normal families and shared values, Bull. London Math. Soc., 2000, 32: 325--331.

[12] Chang J. M., Fang M. L., Normality and shared functions of holomorphic functions and their derivatives, Michigan Math. J., 2005, 53: 625--645.

[13] Xu J. F., Yi H. X., The relation between solutions of higher order differential equation with functions of small growth, Acta Mathematica Sinica, Chinese Series, 2010, 53(2): 291--296.

[14] Huang Z. B., Chen Z. X., Subnormal solutions of second order homogeneous linear differential equations with periodic coefficients, Acta Mathematica Sinica, Chinese Series, 2009, 52(1): 9--16.

[15] Chang J. M., Fang M. L., Zalcman L., Normal families of holomorphic functions, Illinois Journal of Mathematics., 2004, 48: 319--337.

基金

国家自然科学基金资助项目(10771121);广东省自然科学基金(9452902001003278)及广东省高校优秀青年创新人才培养项目(LYM08097)

PDF(468 KB)

364

Accesses

0

Citation

Detail

段落导航
相关文章

/