An integral functional equation on groups under two measures.

• Fadli, B. ^[1] ; Zeglami, D. ^[2] ; Kabbaj, S. ^[1]
  1. [1] Université Ibn-Tofail

     Université Ibn-Tofail

     Kenitra, Marruecos

     
  2. [2] Moulay Ismail University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 3, 2018, págs. 565-581
• Idioma: inglés
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• Resumen

  • 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.