整函数与其差分算子的唯一性定理

刘慧芳, 毛志强

数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 825-832.

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数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 825-832. DOI: 10.12386/A2015sxxb0081
论文

整函数与其差分算子的唯一性定理

    刘慧芳1, 毛志强2
作者信息 +

Uniqueness Theorems on Entire Functions and Their Difference Operators

    Hui Fang LIU1, Zhi Qiang MAO2
Author information +
文章历史 +

摘要

本文证明了:如果有限级非常数整函数 f 和它的差分算子Δηnf CM分担小函数α, 且0为f的亏值, 那么(Δηnf-α)/(f-α) ≡ c, 其中 c 为非零常数.同时, 还研究了整函数f 和它的差分算子Δηf, Δηnf CM分担小函数α的唯一性问题.

Abstract

Let f be a non-constant entire function of finite order, and α be a small function with respect to f. We prove that if f and its difference operator Δηnf share α CM and 0 is a deficient value of f, then (Δηnf-α)/(f-α) ≡ c for some non-zero constant c. We also consider the uniqueness of entire function f sharing α CM with its difference operators Δηf and Δηnf.

关键词

整函数 / 小函数 / 差分算子 / 唯一性

Key words

entire function / small function / difference operator / uniqueness

引用本文

导出引用
刘慧芳, 毛志强. 整函数与其差分算子的唯一性定理. 数学学报, 2015, 58(5): 825-832 https://doi.org/10.12386/A2015sxxb0081
Hui Fang LIU, Zhi Qiang MAO. Uniqueness Theorems on Entire Functions and Their Difference Operators. Acta Mathematica Sinica, Chinese Series, 2015, 58(5): 825-832 https://doi.org/10.12386/A2015sxxb0081

参考文献

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基金

国家自然科学基金(11201195,11171119);江西省自然科学基金(20132BAB201008,20122BAB201012)

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