International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 13-16, Pages 847-859
doi:10.1155/S0161171204304254
On Cauchy-type functional equations
Elqorachi Elhoucien1
and Mohamed Akkouchi2
1Department of Mathematics, Faculty of Sciences, University of Ibnou Zohr, Agadir 80000, Morocco
2Department of Mathematics, Faculty of Sciences, Semlalia, University of Cadi Ayyad, Marrakech 40000, Morocco
Abstract
Let G be a Hausdorff topological locally compact group. Let M(G) denote the Banach algebra of all complex and bounded measures on G. For all integers n≥1 and all μ∈M(G), we consider the functional equations ∫Gf(xty)dμ(t)=∑i=1ngi(x)hi(y), x,y∈G, where the functions f, {gi}, {hi}: G→ℂ to be determined are bounded and continuous functions on G. We show how the solutions of these equations are closely related to the solutions of the μ-spherical matrix functions. When G is a compact group and μ is a Gelfand measure, we give the set of continuous solutions of these equations.