On the permutability of entire functions
type: Item
instance of: scholarly article
title: On the permutability of entire functions
zbMATH Open document ID: 0774.30029
DOI: 10.1016/0022-247X(92)90242-6
author: Jian-Hua Zheng
author: Chungchun Yang
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-01-16T00:00:00Z
review text: Some results are proved in this paper which seem to support the following conjecture: Any entire function of finite order that is permutable with a periodic entire function must be itself periodic. The most important result in this paper concerning this conjecture is for \(F(z)\exp(Q(z))\) where both \(P(z)\) and \(Q(z)\) are non constant polynomials and \(P(0)\neq 0\). In this case, if \(H(z)\) is entire, \(H(F(0))\neq 0\), and permutable with \(F(e^ z)\) then \(H(z)\) is periodic and has the form \(H(z)=G(e^{z/s})\) for some entire function \(G\) and positive integer \(s\). A separated deep result of the paper says that the only entire function of finite order that is permutable with \(\cos\sqrt z\) is \(\cos\sqrt z\) itself.
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 91577
zbMATH Keywords: permutable
zbMATH Keywords: periodic
reviewed by: László Máté
MaRDI profile type: Publication
cites work: Q5622513
cites work: On Factorization of Meromorphic Functions
cites work: Q5683031
cites work: Q5723337
cites work: Permutability and unique factorizability of certain entire functions
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description: scientific article; zbMATH DE number 91577