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On Bessel-Riesz operators
dc.contributor.author | Cerutti, Rubén Alejandro | |
dc.date.accessioned | 2023-06-12T12:01:37Z | |
dc.date.available | 2023-06-12T12:01:37Z | |
dc.date.issued | 2007 | |
dc.identifier.citation | Cerutti, Rubén, 2007. On Bessel-Riesz operators. FACENA. Corrientes: Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura, vol. 23, p. 17-27. ISSN 1851-507X. | es |
dc.identifier.issn | 1851-507X | es |
dc.identifier.uri | http://repositorio.unne.edu.ar/handle/123456789/51668 | |
dc.description.abstract | This article deals with certain kind of potential operator defined as convolution with the generalized function Wα (P ± i0,m,n)depending on a complex parameter α and a real non negative one m. The definitory formulae and several properties of the family {W (P ± i m n)} α∈C α 0, , α; have been introduced and studied by Trione (see [14]) specially the important followings two: a) Wα ∗Wβ =Wα+β , α and β complex numbers, and b) k W −2 is a fundamental solution of the k-times iterated Klein-Gordon operator Writing Wα (P ± i0,m,n) as an infinite linear combination of the ultrahyperbolic Riesz kernel of different orders Rα (P ± i0)which is a causal (anticausal) elementary solution of the ultrahyperbolic differential operator and taking into account its Fourier transform it is possible to evaluate the Fourier transform of the kernel Wα (P ± i0,m,n). We prove the composition formula Wα ∗Wβϕ =Wα+βϕ for a sufficiently good function. The proof of this result is based on the composition formulae presented by Trione in [14], but we also present a different way. Other simple property studied is the one that establish the relationship between the ultrahyperbolic Klein-Gordon operator and the Wα Bessel-Riesz operator. Finally we obtain an expression that will be consider a fractional power of the Klein-Gordon operator. | es |
dc.format | application/pdf | es |
dc.format.extent | p. 17-27 | es |
dc.language.iso | spa | es |
dc.publisher | Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura | es |
dc.rights | openAccess | es |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/ar/ | es |
dc.source | FACENA, 2007, vol. 23, p. 17-27. | es |
dc.subject | Bessel-Riesz potentials | es |
dc.subject | Fractional derivative | es |
dc.subject | Hypersingular integral | es |
dc.title | On Bessel-Riesz operators | es |
dc.type | Artículo | es |
unne.affiliation | Fil: Cerutti, Rubén Alejandro. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina. | es |
unne.journal.pais | Argentina | es |
unne.journal.ciudad | Corrientes | es |
unne.journal.volume | 23 | es |
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