| 涉及整函数差分算子的唯一性定理 |
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| 引用本文： | 陈创鑫,张然然. 涉及整函数差分算子的唯一性定理[J]. 数学年刊A辑(中文版), 2021, 42(1): 11-22 |
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| 作者姓名： | 陈创鑫 张然然 |
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| 作者单位： | 仲恺农业工程学院计算科学学院, 广州 510225;广东第二师范学院数学系, 广州 510303. |
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| 基金项目： | 国家自然科学基金(No.,11801093), 广东省青年创新人才项目(No.,2018KQNCX117),广东省特色创新项目(No.,2019KTSCX119)和广东省自然科学基金(No.,2018A030313508, No.,2020A1515010459) |
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| 摘 要： | 作者研究了关于有穷级整函数两个差分算子的分担值问题,证明了:令f(z)是满足λ(f-a(z))＜p(f)的有穷级超越整函数,其中a(z)(∈ S(f))是整函数且满足p(a(z))＜1,并令η(∈C)是常数且满足Δ2ηf(z)≠0.如果Δ2ηf(z)和Δηf(z)CM分担Δηa(z),其中Δηa(z)∈S(Δ2ηf(z...
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| 关 键 词： | 差分算子 整函数 Borel例外值 分担值 |
| 收稿时间： | 2020-03-19 |
| 修稿时间： | 2020-09-24 |
Uniqueness Theorems Related to Difference Operators of Entire Functions |
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| CHEN Chuangxin,ZHANG Ranran. Uniqueness Theorems Related to Difference Operators of Entire Functions[J]. Chinese Annals of Mathematics, 2021, 42(1): 11-22 |
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| Authors: | CHEN Chuangxin ZHANG Ranran |
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| Affiliation: | College of Computational Sciences, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, China. E-mail: chenchxin@126.com; Corresponding author. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China. E-mail: zhangranran@gdei.edu.cn |
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| Abstract: | In this paper,the authors study the shared-value problem concerning two difference operators of an entire function with finite order.They prove that:Let f(z)be a finite order transcendental entire function such thatλ(f-a(z))<ρ(f),where a(z)(∈S(f))is an entire function and satisfiesρ(a(z))<1,and letη(∈C)be a constant such thatΔ2ηf(z)≠0.IfΔ2ηf(z)andΔηf(z)shareΔηa(z)CM,whereΔηa(z)∈S(Δ2ηf(z)),then f(z)=a(z)+BeAz,where A,B are two nonzero constants and a(z)reduces to a constant. |
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| Keywords: | Difference operator Entire function Borel exceptional value Sharing value |
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