The generalized Van Vleck's equation on locally compact groups.

• Autores: B. Fadli, D. Zeglami, S. Kabbaj
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 36, Nº. 4, 2017, págs. 545-566
• Idioma: inglés
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• Resumen

  • We determine the continuous solutions ʄ, g :G → C of each of the two functional equations ∫G{ʄ,(xyt) – ʄ(σ(y)xt)}dμ(t) = ʄ(x)g(y),   x, y ∈ G, ∫G{ʄ,(xyt) – ʄ(σ(y)xt)}dμ(t) = g(x)ʄ(y),   x, y ∈ G, where G is a locally compact group, σ is a continuous involutive automorphism on G, and μ is a compactly supported, complex-valued Borel measure on G.