Study of some functional equations related to some algebras of matrices

• Autorzy: Akkouchi M. , Rhali M.
• Języki publikacji: EN

Abstrakty

EN

Let K be the real or complex field. Let 1 < n < p be two positive integers. We denote Mp(K) the usual algebra of p x p-matrices. Let An be an n- dimensional subalgebra of Mp(K). Then there exists an injective linear mapping A : Kn- Mp(K) such that A^") = An' Therefore K" may be equipped with a product denoted * such that (Kn, +,*) is an associative algebra. The aim of this paper is to investigate the general solutions of the functional equation: f(x*y) = f(x) f(y), and its Pexider form f(x*y) = g(x) h(y), for all x, y in Kn, where f,g, h: Kn - K are unknown functions. This work is inspired by the paper [2].

Słowa kluczowe

EN

usual algebra; functional equations; multiplicative function; algebra of matrices

PL

algebra zwykła; funkcja multiplikatywna; równania funkcjonalne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 3
• Strony: 611--622
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Akkouchi M.

• Department of Mathematics, University Cadi Ayyad, Faculty of Sciences - Semlalia, P.O. Box: 2390, Marrakesh, Morocco (Maroc)

autor

Rhali M.

• Department of Mathematics, University Cadi Ayyad, Faculty of Sciences - Semlalia, P.O. Box: 2390, Marrakesh, Morocco (Maroc)

Bibliografia

• [1] J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.
• [2] J. K. Chung and P. K. Sahoo, General solution of some functional equations related to the determinant of some symmetric matrices, Demonstratio Math. 35 (2002), No. 3, 539-544.
• [3] P. K. Sahoo and T. Riedel, Mean Value Theorems and Functional Equations, World Scientific, Singapore, 1998.