| 邓炳茂,刘丹,方明亮.亚纯函数与其差分的唯一性[J].数学年刊A辑,2018,(4):341~348 |
| 亚纯函数与其差分的唯一性 |
| Unicity of Meromorphic Functions and Their Difference Operators |
| Received:March 24, 2017 Revised:December 10, 2017 |
| DOI：10.16205/j.cnki.cama.2018.0029 |
| 中文关键词: Shared polynomial, Uniqueness, Difference operators |
| 英文关键词:Shared polynomial, Uniqueness, Difference operators |
| 基金项目: |
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| 中文摘要: |
| 研究了亚纯函数与其差分算子分担多项式的唯一性问题, 证明了:
设$f$是一个有穷级非常数亚纯函数, $p(z)(\not\equiv 0)$ 是一个多项式.
如果$f, \Delta_cf$ 与$\Delta_{c}^{2}f$ CM 分担$\infty$, $ p(z)$, 则$f\equiv\Delta_cf$ 或
$f(z)=\rme^{Az+B}+b$, 其中$p(z)\equiv b\neq 0$, $A\neq 0$ 满足$\rme^{Ac}=1$.
本文结果是对Chang, Fang(Chang J M, Fang M L. Uniqueness of entire functions and fixed points [J]. {\it Kodai Math J}, 2002, 25(1): 309--320.)结果的差分模拟,
并且完整回答了Chen, Chen(Chen B Q, Chen Z X, Li S. Uniqueness theorems on entire functions and their difference
operators or shifts [J]. {\it Abstr Appl Anal}, 2012, Art. ID 906893, 8 pp.)的问题. |
| 英文摘要: |
| This paper deals with the unicity of meromorphic functions and their difference operators and proves:
Let $f$ be a nonconstant meromorphic function of finite order, and let $p(z)(\not\equiv 0)$ be
a polynomial. If $f, \Delta_cf$ and $\Delta_{c}^{2}f$ share $\infty$ and $ p(z)$ CM, then either $f\equiv\Delta_cf$ or $f(z)=\rme^{Az+B}+b$, where $p(z)\equiv b\neq 0$, $A\neq 0$ satisfying $\rme^{Ac}=1$.
Our result provides a difference analogue of a result of Chang and Fang (Chang J M, Fang M L. Uniqueness of entire functions and
fixed points [J]. {\it Kodai Math J}, 2002, 25(1): 309--320.), and answers the question of Chen and Chen (Chen B Q, Chen Z X, Li S. Uniqueness theorems on entire functions and their difference
operators or shifts [J]. {\it Abstr Appl Anal}, 2012, Art ID 906893, 8 pp.). |
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