Generalized Delta coherent pairs

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dc.contributor.author Kwon, Kil H.
dc.contributor.author Lee, J. H.
dc.contributor.author Marcellán Español, Francisco José
dc.date.accessioned 2009-12-07T09:55:29Z
dc.date.available 2009-12-07T09:55:29Z
dc.date.issued 2004
dc.identifier.bibliographicCitation Journal of the Korean Mathematical Society, 2004, vol. 41, n. 6, p. 977-994
dc.identifier.issn 0304 - 9914
dc.identifier.uri http://hdl.handle.net/10016/5970
dc.description 18 pages, no figures.-- MSC2000 codes: 42C05, 33C45.
dc.description MR#: MR2095548 (2005k:33007)
dc.description Zbl#: Zbl 1058.42018
dc.description.abstract A 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.abstract We 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.sponsorship The 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.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Korean Mathematical Society
dc.rights © Korean Mathematical Society
dc.subject.other Discrete orthogonal polynomials
dc.subject.other Delta-coherent pairs
dc.title Generalized Delta coherent pairs
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.relation.publisherversion http://www.mathnet.or.kr/mathnet/kms_content.php?no=366087
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
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