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Generalized Delta coherent pairs

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorKwon, Kil H.
dc.contributor.authorLee, J. H.
dc.contributor.authorMarcellán Español, Francisco José
dc.date.accessioned2009-12-07T09:55:29Z
dc.date.available2009-12-07T09:55:29Z
dc.date.issued2004
dc.description18 pages, no figures.-- MSC2000 codes: 42C05, 33C45.
dc.descriptionMR#: MR2095548 (2005k:33007)
dc.descriptionZbl#: Zbl 1058.42018
dc.description.abstractA pair of quasi-definite linear functionals ${u_0,u_1}$ is a generalized $Delta$-coherent pair if monic orthogonal polynomials $${P_n(x)}_{n=0} nfty$$ and $${R_n(x)}_{n=0} nfty$$ relative to $u_0$ and $u_1$, respectively, satisfy a relation $$ R_n(x) = frac{1}{n+1}Delta P_{n+1}(x)-frac{sigma_n}{n}Delta P_n(x)- frac{ au_{n-1}}{n-1}Delta P_{n-1}(x), ~~ ngeq 2,$$ where $sigma_n$ and $ au_n$ are arbitrary constants and $Delta p=p(x+1)-p(x)$ is the difference operator.
dc.description.abstractWe show that if ${u_0,u_1}$ is a generalized $Delta$-coherent pair, then $u_0$ and $u_1$ must be discrete-semiclassical linear functionals. We also find conditions under which either $u_0$ or $u_1$ is discrete-classical.
dc.description.sponsorshipThe first author (KHK) was partially supported by KOSEF(R01{1999{00001). The second author(JHL) was supported by BK Postdoctoral Program in SNU. The work of the third author (FM) was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant BFM2000-0206-C04-01.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of the Korean Mathematical Society, 2004, vol. 41, n. 6, p. 977-994
dc.identifier.issn0304 - 9914
dc.identifier.urihttps://hdl.handle.net/10016/5970
dc.language.isoeng
dc.publisherKorean Mathematical Society
dc.relation.publisherversionhttp://www.mathnet.or.kr/mathnet/kms_content.php?no=366087
dc.rights© Korean Mathematical Society
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherDiscrete orthogonal polynomials
dc.subject.otherDelta-coherent pairs
dc.titleGeneralized Delta coherent pairs
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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