Publication: A canonical family of multiple orthogonal polynomials for Nikishin systems

 dc.affiliation.dpto UC3M. Departamento de Matemáticas es dc.affiliation.grupoinv UC3M. Grupo de Investigación: Análisis Aplicado es dc.contributor.author López Lagomasino, Guillermo dc.contributor.author Álvarez Rocha, Ignacio dc.date.accessioned 2010-01-14T10:46:56Z dc.date.available 2010-01-14T10:46:56Z dc.date.issued 2009-12 dc.description 16 pages.-- MSC2000 codes: Primary 42C05, 33C25; Secondary 41A21.-- Submitted paper. dc.description.abstract For any pair of compact intervals Δ1 and Δ2 of the real line such that Δ1∩Δ2 = ø we obtain two pairs of absolutely continuous probability measures (μ1,μ2) and (τ1,τ2) supported on Δ1 and Δ2, respectively, such that: dc.description.abstract - for appropriate constants C1 and C2, (μ1,μ2) is the Nikishin system generated by (μ1,C1τ1) and (τ1,τ2) the Nikishin system generated by (τ1,C2μ1), dc.description.abstract - the polynomials of multiple orthogonality with respect to the Nikishin system (μ1,μ2) and indices {..., (n,n), (n+1,n), ...} satisfy a recurrence relations with constant coe±cients of period 2, dc.description.abstract - 1/hat-μ1(z) and 1/hat-μ2(z) are the functions which describe the ratio asymptotics of multiple orthogonal polynomials with respect to an arbitrary Nikishin system N(σ1,σ2) verifying supp(σi) = Δi, and σi' > 0, i = 1,2, almost everywhere on Δi. Analogously, 1/hat-τ1(z) and 1/hat-τ2(z) give the ratio asymptotics for N(σ1,σ2). dc.description.sponsorship The research of both authors was supported by research grant MTM 2006-13000-C03-02 of Ministerio de Ciencia e Innovación, Spain. I.A. Rocha also received support from Universidad Politécnica de Madrid through Grupo de Investigación TACA. dc.description.status No publicado dc.format.mimetype application/pdf dc.identifier.uri https://hdl.handle.net/10016/6394 dc.language.iso eng dc.rights.accessRights open access dc.subject.eciencia Matemáticas dc.subject.other Hermite-Padé orthogonal polynomials dc.subject.other Multiple orthogonal polynomials dc.subject.other Nikishin system dc.subject.other Varying measures dc.subject.other Ratio asymptotics dc.title A canonical family of multiple orthogonal polynomials for Nikishin systems dc.type research article * dc.type.review NonPeerReviewed dspace.entity.type Publication
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