Iterative characterizations of powers and exponentials
type: Item
instance of: scholarly article
title: Iterative characterizations of powers and exponentials
zbMATH Open document ID: 0669.30016
DOI: 10.1007/BF01836444
published in: Aequationes Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137300
review text: 1. The only non-constant entire function satisfying the functional equation \[ F(z+F(z))=F(z)F(z^{k-1}+1), \] where \(k\geq 3\) is a fixed integer, is \(F(z)=z^ k.\) 2. The only non-constant entire functions satisfying the functional equation \[ F(z+F(z))=F'(F(z)F'(z)) \] are \(a^{-2} \exp (az)\), where a is an arbitrary non-zero complex constant. The second result seems harder to prove and depends on an application of Nevanlinna theory.
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 4095836
zbMATH Keywords: entire function
zbMATH Keywords: functional equation
author: Sanford L. Segal
MaRDI profile type: Publication
cites work: Q5622513
cites work: Q3671491
cites work: Q5723337
cites work: Multiplication Rules for Polynomials
cites work: Q3940060
cites work: On Nathanson's functional equation
OpenAlex ID: W1984009871
description: scientific article; zbMATH DE number 4095836