亚纯函数与其差分的唯一性  

Unicity of Meromorphic Functions and Their Difference Operators

作　　者：邓炳茂[1] 刘丹[1] 方明亮[1] DENG Bingmao;LIU Dan;FANG Mingliang(Institute of Applied Mathematics,South China Agricultural University,Guangzhou 510642,China)

机构地区：[1]华南农业大学应用数学研究所,广州510642

出　　处：《数学年刊（A辑）》2018年第4期341-348,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11371149;No.11701188);华南农业大学博士研究生境外联合培养项目(No.2017LHPY003)的资助

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)(■0)是一个多项式.如果f,△_cf与△_c^2f CM分担∞,p(z),则f≡△_cf或f(z)=e^(Az+B)+b,其中p(z)≡b≠0,A≠0满足e^(Ac)=1.本文结果是对Chang, Fang(Chang J M, Fang M L. Uniqueness of entire functions and fixed points [J]. 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]. Abstr Appl Anal, 2012,Art. ID 906893, 8 pp.)的问题.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 letp(z)(■=0)be a polynomial.If f,△cf and △^2cf share ∞ and p(z)CM,the either f≡△cf or f(z)=e^Az+B+b,where p(z)≡b≠0,A≠0 satisfying e^Ac=1.Our result provides a difference analogue of a result of Chang and Fang(Chiang J M,Fang M L.Uniqueness of entire functions and fixed points[J].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].Abstr Appl Anal,2012,Art ID 906893, 8pp.).

关 键 词：分担多项式 唯一性 差分算子 

分 类 号：O174.52[理学—数学]