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.