On the factorization of several classes of entire functions
type: Item
instance of: scholarly article
title: On the factorization of several classes of entire functions
zbMATH Open document ID: 0635.30027
published in: Kodai Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The author proves some interesting theorems on factorization of entire functions under composition. For example he proves: Let \[ F(z)=H(z)+\exp (\lambda z+G(z)), \] where both H(z) and G(z) are periodic entire functions with period \(\tau\) and \(\lambda\tau\) /\(\pi\) i is an irrational number. If \(F(z)=f(g)\), where both f and g are non-linear entire functions, then we have the forms of f and g, respectively, \[ f(w)=H_ 1(w)+\exp (cw+H_ 2(w)),\quad g(z)=dz+H_ 3(z), \] where \(dc=\lambda\), both \(H_ 1\) and \(H_ 2\) are periodic functions with period \(d\tau\) and \(H_ 3\) is periodic with period \(\tau\).
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 4034080
zbMATH Keywords: factorization
zbMATH Keywords: periodic entire functions
author: Jian-Hua Zheng
reviewed by: Fred Gross
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037463
OpenAlex ID: W2017446683
cites work: Prime Entire Functions
cites work: Uniqueness of the factorization under composition of certain entire functions
cites work: Q3890961
cites work: Meromorphic Functions with Three Radially Distributed Values
cites work: On Factorization of Meromorphic Functions
cites work: On pseudo-primality of the \(n\)-th power of prime entire functions
cites work: On the Periodicity of f(g)
DOI: 10.2996/KMJ/1138037463
description: scientific article; zbMATH DE number 4034080