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http://hdl.handle.net/10662/16351
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Campo DC | Valor | idioma |
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dc.contributor.author | Akkouchi, Mohamed | - |
dc.contributor.author | Bakali, Allal | - |
dc.contributor.author | Bouikhalene, Belaid | - |
dc.contributor.author | Elqorachi, Elhoucien | - |
dc.date.accessioned | 2022-12-02T12:42:00Z | - |
dc.date.available | 2022-12-02T12:42:00Z | - |
dc.date.issued | 2006 | - |
dc.identifier.issn | 0213-8743 | - |
dc.identifier.uri | http://hdl.handle.net/10662/16351 | - |
dc.description.abstract | 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. | es_ES |
dc.format.extent | 16 p. | es_ES |
dc.format.mimetype | application/pdf | en_US |
dc.language.iso | eng | es_ES |
dc.publisher | Universidad de Extremadura, Servicio de Publicaciones | es_ES |
dc.rights | Attribution-NonCommercial 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc/4.0/ | * |
dc.subject | Ecuación funcional | es_ES |
dc.subject | Medida de Gelfand | es_ES |
dc.subject | Función μ-esférica | es_ES |
dc.subject | Denición positiva función finita | es_ES |
dc.subject | Teoría de la representación | es_ES |
dc.subject | Operador diferencial invariante | es_ES |
dc.subject | Functional equation | es_ES |
dc.subject | Gelfand measure | es_ES |
dc.subject | μ-spherical function | es_ES |
dc.subject | Positive deninite function | es_ES |
dc.subject | Representation theory | es_ES |
dc.subject | Lie group | es_ES |
dc.title | On generalized d’Alembert functional equation | es_ES |
dc.type | article | es_ES |
dc.description.version | peerReviewed | es_ES |
europeana.type | TEXT | en_US |
dc.rights.accessRights | openAccess | es_ES |
dc.subject.unesco | 1202.08 Ecuaciones Funcionales | es_ES |
dc.subject.unesco | 1210.08 Grupos de Lie | es_ES |
europeana.dataProvider | Universidad de Extremadura. España | es_ES |
dc.identifier.bibliographicCitation | AKKOUCHI, M. , BAKALI, A. , BOUIKHALENE, B. y ELQORACHI, E. (2006). On generalized d’Alembert functional equation. Extracta Mathematicae, 21 (1) 67-82. E-ISSN 2605-5686 | es_ES |
dc.type.version | publishedVersion | es_ES |
dc.contributor.affiliation | University Cadi Ayyad. Morocco | es_ES |
dc.contributor.affiliation | Ibn Zohr University. Morocco | - |
dc.contributor.affiliation | University Ibn Tofail. Morocco | - |
dc.identifier.publicationtitle | Extracta Mathematicae | es_ES |
dc.identifier.publicationissue | 1 | es_ES |
dc.identifier.publicationfirstpage | 67 | es_ES |
dc.identifier.publicationlastpage | 82 | es_ES |
dc.identifier.publicationvolume | 21 | es_ES |
dc.identifier.e-issn | 2605-5686 | - |
Colección: | Extracta Mathematicae Vol. 21, nº 1 (2006) |
Archivos
Archivo | Descripción | Tamaño | Formato | |
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2605-5686_21_1_67.pdf | 173,35 kB | Adobe PDF | Descargar |
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