Permutability of entire functions
type: Item
instance of: scholarly article
title: Permutability of entire functions
zbMATH Open document ID: 0767.30024
author: Jian-Hua Zheng
author: Chungchun Yang
published in: Kodai Mathematical Journal
publication date: 1993-05-16T00:00:00Z
full work available at URL: kodai9211.pdf
review text: The authors prove a number of results on permutability of entire functions. Their main result follows: Theorem. Let \(f(z)=\text{sin } z+Q(z)\), where \(Q(z)\) is a polynomial and \(g(z)\) is a nonlinear entire function of finite order, which is permutable with \(f(z)\). Then (i) when \(\deg Q=0\), \(g=f\) or \(g=-\text{sin }z+\kappa\pi\), \(f=\text{sin }z+\lambda\pi\); (ii) when \(\deg Q=1\), \(g=f+2\kappa\pi\) or \(-f+2\kappa\pi\) for some integer \(\kappa\); (iii) when \(\deg Q>1\) and \(Q(z)\not\equiv-Q(- z)\), then \(g=f\); (iv) when \(\deg Q>1\) and \(Q(z)\equiv-Q(-z)\), then \(g=f\) or \(-f\).
reviewed by: Fred Gross
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 167941
zbMATH Keywords: permutability of entire functions
MaRDI profile type: Publication
OpenAlex ID: W2017409264
cites work: Q5683031
cites work: Permutability and unique factorizability of certain entire functions
cites work: Q3890961
cites work: Q3310111
cites work: Permutability of entire functions satisfying certain differential equations
DOI: 10.2996/KMJ/1138039599
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description: scientific article; zbMATH DE number 167941