涉及整函数差分算子的唯一性定理  

Uniqueness Theorems Related to Difference Operators of Entire Functions

作　　者：陈创鑫[1] 张然然 CHEN Chuangxin;ZHANG Ranran(College of Computational Sciences,Zhongkai University of Agriculture and Engineering,Guangzhou 510225,China;Corresponding author.Department of Mathematics,Guangdong University of Education,Guangzhou 510303,China)

机构地区：[1]仲恺农业工程学院计算科学学院,广州510225 [2]广东第二师范学院数学系,广州510303

出　　处：《数学年刊（A辑）》2021年第1期11-22,共12页Chinese Annals of Mathematics

基　　金：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);广东省自然科学基金(No.2018A030313508,No.2020A1515010459)的资助。

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))<ρ(f)的有穷级超越整函数,其中a(z)(∈S(f))是整函数且满足ρ(a(z))<1,并令η(∈C)是常数且满足△^(2)_(η)f(z)≠0.如果△^(2)_(η)f(z)和Δ_(η)f(z)CM分担Δ_(η)a(z),其中Δ_(η)a(z)∈S(Δ^(2)_(η)f(z)),那么f(z)=a(z)+Be^(Az),其中A,B是两个非零常数且a(z)退化为常数.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 thatΔ^(2)_(η)f(z)≠0.IfΔ^(2)_(η)f(z)andΔ_(η)f(z)shareΔ_(η)a(z)CM,whereΔ_(η)a(z)∈S(Δ^(2)_(η)f(z)),then f(z)=a(z)+Be^(Az),where A,B are two nonzero constants and a(z)reduces to a constant.

关 键 词：差分算子 整函数 BOREL例外值 分担值 

分 类 号：O152.1[理学—数学]