D'Alembert's and Wilson's functional equations on step 2 nilpotent groups
type: Item
instance of: scholarly article
title: D'Alembert's and Wilson's functional equations on step 2 nilpotent groups
zbMATH Open document ID: 1054.39017
published in: Aequationes Mathematicae
publication date: 2004-10-05T00:00:00Z
review text: The author extends his work [Aequationes Math. 59, 306--320 (2000; Zbl 0959.39023)] about complex valued solutions \(f\) of d'Alembert's functional equation \(f(x+y)+f(x-y)=2f(x)f(y)\) to complex valued solutions \(f,g\) of Wilson's equation \(f(x+y)+f(x-y)=2f(x)g(y)\) on ``step 2 nilpotent groups''. They were called metabelian groups in the previous paper and are groups whose commutator subgroup is subset of their center. These groups are chosen because they are close to abelian groups but the author offers on them solutions of the two above mentioned functional equations that are essentially different of those in the abelian case.
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 2106521
zbMATH Keywords: d'Alembert functional equation
zbMATH Keywords: nilpotent groups
zbMATH Keywords: complex valued solutions
zbMATH Keywords: metabelian groups
zbMATH Keywords: Wilson's functional equation
author: Henrik Stetkær
reviewed by: János Aczél
MaRDI profile type: Publication
full work available at URL: s00010-003-2715-5
OpenAlex ID: W1596235764
DOI: 10.1007/S00010-003-2715-5
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description: scientific article; zbMATH DE number 2106521