| 孟晓仁,曹廷彬.多复变整函数涉及全导数的唯一性定理[J].数学年刊A辑,2014,35(2):203~210 |
| 多复变整函数涉及全导数的唯一性定理 |
| A Uniqueness Theorem for Entire Functions Concerning the Total Derivative inSeveral Complex Variables |
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| DOI： |
| 中文关键词: 唯一性定理, 全导数, 整函数, 多复变 |
| 英文关键词:Uniqueness theorem, Total derivative, Entire function, Several complex variables |
| 基金项目:国家自然科学基金 (No.11101201), 江西省自然科学基金(No.20122BA211001)和江西省教育厅自然科学基金(No.GJJ13077) |
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| 中文摘要: |
| 结合金路提出的多复变上整函数全导数的概念, 得到了如下定理:
对于 $n$ 维复欧式空间$\mathbb{C}^{n}$上两个非常数整函数$f$和$g$, 以及一个正整数$k$,
如果$\delta(0, f)+\delta(0, g)>1$, $D^{k}f=1\Leftrightarrow
D^{k}g=1$, 那么$f\equiv g$.
这一结论是仪洪勋和杨重骏的定理的推广. |
| 英文摘要: |
| The authors use the concept of the total
derivative of entire functions in several complex variables due to
Jin, and obtain that
for two nonconstant entire functions $f$ and $g$ on $\mathbb{C}^{n}$
and a positive integer $k, $ if $\delta(0, f)+\delta(0, g)>1$ and
$D^{k}f=1\Leftrightarrow D^{k}g=1$, then $f\equiv g. $ This
result is an extension of a result of Yi and Yang. |
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