On factorization of meromorphic functions
On factorization of meromorphic functions
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DOI：
10.1090/s0002-9947-1968-0220936-0
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发表时间：
1968
影响因子：
1.3
通讯作者：
F. Gross
中科院分区：
文献类型：
--
作者：
F. Gross
1. 简介。亚纯函数 h (z)= f (g (z)) 被称为分别以 f (z) 和 g (z) 作为左因子和右因子，前提是 f (z) 是非线性且亚纯的，g (z) 是非线性且完整的（当 f (z) 是有理数时 g 可以是亚纯的）。如果上述形式的每个因式分解都意味着其中一个函数，则 h (z) 被称为素数（伪素数）。 f (z) 或 g (z) 是线性的（多项式或 f (z) 是有理数）。关于亚纯函数的因式分解，人们可以提出许多问题。我们将主要关注其中的两个。 1. 给定的亚纯函数有多少个因子？ 2. 给定亚纯函数的某些性质，其因子有哪些相关性质？
1. Introduction. A meromorphic function h (z)= f (g (z)) is said to have f (z) and g (z) as left and right factors respectively, provided that f (z) is nonlinear and meromorphic and g (z) is nonlinear and entire (g may be meromorphic when f (z) is rational). h (z) is said to be prime (pseudo-prime) if every factorization of the above form implies that one of the functions. f (z) or g (z) is linear (a polynomial or f (z) is rational).There are numerous questions that one can ask about factorization of meromorphic functions. We shall primarily be concerned with two of them. 1. How many factors does a given meromorphic function have? 2. Given certain properties of a meromorphic function, what are some related properties of its factors?