On the equation P(f) = Q(g), where P, Q are polynomials and f, g are entire functions
On the equation P(f) = Q(g), where P, Q are polynomials and f, g are entire functions
复制标题
在方程 P(f) = Q(g) 上，其中 P、Q 是多项式，f、g 是完整函数
DOI：
10.1353/ajm.2010.a404142
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发表时间：
2008
影响因子：
1.7
通讯作者：
F. Pakovich
中科院分区：
文献类型：
--
作者：
F. Pakovich
在1922年里特描述了多项式的解决方案的功能方程P（f）= Q（g）。在本文中，我们描述的解决方案的情况下，$P，Q$是多项式，而$f，g$允许是任意整函数。事实上，我们描述了更一般的函数方程$s = P（f）= Q（g）的解，$其中$s，f，g$是整函数，$P，Q$是任意有理函数。作为应用，我们解决了整函数的“强唯一多项式”的描述问题。
In 1922 Ritt described polynomial solutions of the functional equation $P(f) = Q(g).$ In this paper we describe solutions of the equation above in the case when $P, Q$ are polynomials while $f, g$ are allowed to be arbitrary entire functions. In fact, we describe solutions of the more general functional equation $s = P(f) = Q(g),$ where $s, f, g$ are entire functions and $P, Q$ are arbitrary rational functions. As an application we solve the problem of description of "strong uniqueness polynomials" for entire functions.