Functional equations on abelian groups with involution
type: Item
instance of: scholarly article
title: Functional equations on abelian groups with involution
zbMATH Open document ID: 0899.39007
DOI: 10.1007/BF02755452
published in: Aequationes Mathematicae
publication date: 1997-10-09T00:00:00Z
full work available at URL: https://eudml.org/doc/137700
review text: The author investigates generalizations of several functional equations such as d'Alembert's, Wilson's, Jensen's and the functional equation of quadratic functions. The main point is that he replaces terms of the form \(x-y\) by \(x+ \sigma (y)\), where \(\sigma\) is an involution. Moreover a general framework is used which is interesting for itself. The main tool is the notion of a \(K\)-spherical function, where \(K\) is a compact transformation group of a topological group. The paper is very interesting, unifies and generalizes earlier results and shows new perspectives in the considered area.
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1053605
zbMATH Keywords: functional equations on abelian groups
zbMATH Keywords: \(K\)-spherical function
zbMATH Keywords: d'Alembert functional equation
zbMATH Keywords: Wilson functional equation
zbMATH Keywords: Jensen functional equation
zbMATH Keywords: functional equation of quadratic functions
zbMATH Keywords: involution
zbMATH Keywords: topological group
author: Henrik Stetkær
reviewed by: Jens Schwaiger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1053605