A VARIANT OF D'ALEMBERT'S AND WILSON'S FUNCTIONAL EQUATIONS FOR MATRIX VALUED FUNCTIONS

被引：0

作者：

Chahbi, Abdellatif ^{[1
]}

Chakiri, Mohamed ^{[1
]}

Elqorachi, Elhoucien ^{[1
]}

机构：

[1] Ibn Zohr Univ, Fac Sci, Dept Math, Equipe Equat Fonct & Applicat, Agadir, Morocco

来源：

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 39卷 / 03期

关键词：

Topological group; monoid; D'Alembert's equation; Wilson's equation; matrix; automorphism; involution; VECTOR;

D O I：

10.4134/CKMS.c220073

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given M a monoid with a neutral element e . We show that the solutions of d'Alembert's functional equation for n x n matrices Phi(pr, qs) + Phi (sp, rq) = 2 Phi(r, s)Phi(p, q), p, q, r, s is an element of M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation {f(pr, qs) + f(sp, rq) = 2 Phi(r, s)f(p, q), {Phi(p, q) = Phi(q, p), p, q, r, s is an element of M are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3 .

引用

页码：785 / 802

页数：18

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