Quaternion-valued multiplicative functions on semigroups
type: Item
instance of: scholarly article
title: Quaternion-valued multiplicative functions on semigroups
author: Ayoub Ouhabi
author: Driss Zeglami
author: M. Ayoubi
published in: Aequationes Mathematicae
publication date: 2025-01-06T00:00:00Z
review text: Let \(S\) be a semigroup and let \(\mathbb{H}\) denote the skew field of the quaternions. The main aim of this paper is to determine quaternion-valued central multiplicative functions in terms of complex-valued multiplicative functions. To do this, at first they solve the system of functional equations\N\[\Na(xy)= a(x)a(y)-b(x)\overline{b(y)}, \qquad\Nb(xy)= a(x)b(y)+b(x)\overline{a(y)},\N\]\N\(x, y\in S\), where \(a, b \colon S \to\mathbb{C}\) denote the unknown functions and \(a\) is assumed to be central.
reviewed by: Eszter Gselmann
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 7962144
zbMATH Keywords: functional equation
zbMATH Keywords: multiplicative function
zbMATH Keywords: quaternion
zbMATH Keywords: semigroup
MaRDI profile type: Publication
cites work: Q3992445
cites work: d'Alembert's other functional equation
cites work: The cosine and sine addition and subtraction formulas on semigroups
cites work: Functional Equations and Inequalities with Applications
cites work: Matrix homomorphism equations on a class of monoids and non abelian groupoids
cites work: On multiplicative maps
cites work: Functional Equations on Groups
cites work: Quaternions for Computer Graphics
cites work: Quaternions and matrices of quaternions
DOI: 10.1007/S00010-024-01040-W
description: scientific article; zbMATH DE number 7962144