Extensions of the sine addition law on groups
type: Item
instance of: scholarly article
title: Extensions of the sine addition law on groups
zbMATH Open document ID: 1419.39049
published in: Aequationes Mathematicae
publication date: 2019-03-26T00:00:00Z
review text: The purpose of the present paper is to solve the functional equation \[ f(xy) = g_1(x)h_1(y) + \mu(x)h_2(y), \qquad x,y \in G, \tag{1} \] where \(G\) is a group (not necessarily abelian), and \(\mu : G \to \mathbb{C}\) is a prescribed character, while \(f, g_1, h_1, h_2 : G \to \mathbb{C}\) are the unknown functions to be determined. The main task is a discussion of the particular case \[ f(xy) = f(x)\chi(y) + \mu(x)f(y), \qquad x,y \in G, \tag{2} \] of (1), in which both \(\chi\) and \(\mu\) are given characters and \(f : G \to \mathbb{C}\) is the unknown function. The results obtained for Equation (2) enable the authors to solve Equation (1).
reviewed by: Nasrin Eghbali
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 7041939
zbMATH Keywords: functional equation
zbMATH Keywords: sine addition law
zbMATH Keywords: group
zbMATH Keywords: character
author: Henrik Stetkær
MaRDI profile type: Publication
full work available at URL: s00010-018-0584-1
OpenAlex ID: W2884580196
Wikidata QID: Q114852569
cites work: Q3992445
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cites work: Q3827009
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cites work: Q5330937
DOI: 10.1007/S00010-018-0584-1
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description: scientific article; zbMATH DE number 7041939