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Proyecciones (Antofagasta)

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FADLI, B.; ZEGLAMI, D.  and  KABBAJ, S.. An integral functional equation on groups under two measures. Proyecciones (Antofagasta) [online]. 2018, vol.37, n.3, pp.565-581. ISSN 0716-0917.

Let G be a locally compact Hausdorff group, let σ be a continuous involutive automorphism on G, and let μ, ν be regular, compactly supported, complex-valued Borel measures on G. We find the continuous solutions 𝑓 : G → C of the functional equation

in terms of continuous characters of G. This equation provides a common generalization of many functional equations (d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s, Stetkær’s, Van Vleck’s equations...). So, a large class of functional equations will be solved.

Keywords : Functional equation; Van Vleck; Kannappan; involutive automorphism; group character..

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