On Cauchy-type functional equations

Elqorachi Elhoucien and Mohamed Akkouchi

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-13

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 ∫ G f ( x t y ) d μ ( t ) = ∑ i = 1 n g i ( x ) h i ( y ) , x , y ∈ G , where the functions f , { g i } , { h i } : 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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:462421

DOI: 10.1155/S0161171204304254

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