Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case

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dc.contributor.author Abreu, L. D.
dc.contributor.author Marcellán Español, Francisco José
dc.contributor.author Yakubovich, S. B.
dc.date.accessioned 2009-12-02T15:29:25Z
dc.date.available 2009-12-02T15:29:25Z
dc.date.issued 2008-05-15
dc.identifier.bibliographicCitation Journal of Mathematical Analysis and Applications, 2008, vol. 341, n. 2, p. 803-812
dc.identifier.issn 0022-247X
dc.identifier.uri http://hdl.handle.net/10016/5916
dc.description 10 pages, no figures.
dc.description MR#: MR2398249 (2009d:46074)
dc.description Zbl#: Zbl 1139.42005
dc.description.abstract Motivated by the G.H. Hardy's 1939 results [G.H. Hardy, Notes on special systems of orthogonal functions II: On functions orthogonal with respect to their own zeros, J. London Math. Soc. 14 (1939) 37–44] on functions orthogonal with respect to their real zeros λn, n=1,2,... , we will consider, under the same general conditions imposed by Hardy, functions satisfying an orthogonality with respect to their zeros with Jacobi weights on the interval (0,1), that is, the functions f(z)=z^ν F(z), ν in R, where F is entire and,
dc.description.abstract $\int_0 1 f(λ_n t)f(λ_m t)t (1-t) dt=0, α>-1-2ν, β>-1
dc.description.abstract when n≠m. Considering all possible functions on this class we obtain a new family of generalized Bessel functions including Bessel and hyperbessel functions as special cases.
dc.description.sponsorship The work of LDA has been supported by CMUC and FCT post-doctoral grant SFRH/BPD/26078/2005. The work of FM has been supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, MTM 2006-13000-C03-02. The work of SBY has been supported, in part, by the "Centro de Matemática" of the University of Porto.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier
dc.subject.other Zeros of special functions
dc.subject.other Orthogonality
dc.subject.other Jacobi weights
dc.subject.other Mellin transform on distributions
dc.subject.other Entire functions
dc.subject.other Bessel functions
dc.subject.other Hyperbessel functions
dc.title Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jmaa.2007.10.050
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.jmaa.2007.10.050
dc.rights.accessRights openAccess
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Análisis Aplicado
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