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

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorAbreu, L. D.
dc.contributor.authorMarcellán Español, Francisco José
dc.contributor.authorYakubovich, S. B.
dc.date.accessioned2009-12-02T15:29:25Z
dc.date.available2009-12-02T15:29:25Z
dc.date.issued2008-05-15
dc.description10 pages, no figures.
dc.descriptionMR#: MR2398249 (2009d:46074)
dc.descriptionZbl#: Zbl 1139.42005
dc.description.abstractMotivated 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.abstractwhen 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.sponsorshipThe 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.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Mathematical Analysis and Applications, 2008, vol. 341, n. 2, p. 803-812
dc.identifier.doi10.1016/j.jmaa.2007.10.050
dc.identifier.issn0022-247X
dc.identifier.urihttps://hdl.handle.net/10016/5916
dc.language.isoeng
dc.publisherElsevier
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.jmaa.2007.10.050
dc.rights© Elsevier
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherZeros of special functions
dc.subject.otherOrthogonality
dc.subject.otherJacobi weights
dc.subject.otherMellin transform on distributions
dc.subject.otherEntire functions
dc.subject.otherBessel functions
dc.subject.otherHyperbessel functions
dc.titleHardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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