Identificador persistente para citar o vincular este elemento:
http://hdl.handle.net/10662/16351
Títulos: | On generalized d’Alembert functional equation |
Autores/as: | Akkouchi, Mohamed Bakali, Allal Bouikhalene, Belaid Elqorachi, Elhoucien |
Palabras clave: | Ecuación funcional;Medida de Gelfand;Función μ-esférica;Denición positiva función finita;Teoría de la representación;Operador diferencial invariante;Functional equation;Gelfand measure;μ-spherical function;Positive deninite function;Representation theory;Lie group |
Fecha de publicación: | 2006 |
Editor/a: | Universidad de Extremadura, Servicio de Publicaciones |
Resumen: | Let G be a locally compact group. Let 𝜎 be a continuous involution of G and let μ be a complex bounded measure. In this paper we study the generalized d’Alembert functional equation D(μ) ∫ G ƒ (𝓍𝓉𝓎)d μ (𝓉) + ∫ G ƒ (𝓍𝓉𝜎 𝜎 (𝓎)) 𝒹 μ (𝓉) = 2 ƒ (𝓍) ƒ (𝓎) 𝓍, 𝓎 ∈ G, where ƒ: G → C to be determined is a measurable and essentially bounded function. We give some conditions under which all solutions are of the form ≺π(x)ξ,ζ¬+≺π(σ(x))ξ,ζ¬ 2 , where (π, H) is a continuous unitary representation of G such that π(μ) is of rank one and ξ, ζ ∈ H. Furthermore, we also consider the case when f is an integrable solution. In the particular case where G is a connected Lie group, we reduce the solution of D(μ) to a certain problem in operator theory. We prove that the solutions of D(μ) are exactly the common eigenfunctions of some operators associated to a left invariant differential operators on G. |
URI: | http://hdl.handle.net/10662/16351 |
ISSN: | 0213-8743 |
Colección: | Extracta Mathematicae Vol. 21, nº 1 (2006) |
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