# 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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