Recurrence relations and outer relative asymptotics of orthogonal polynomials with respect to a discrete Sobolev type inner product

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dc.contributor.author Marcellán Español, Francisco José
dc.contributor.author Pérez Valero, María Francisca
dc.contributor.author Quintana, Yamilet
dc.contributor.author Urieles, Alejandro
dc.date.accessioned 2016-07-12T09:44:45Z
dc.date.available 2016-07-12T09:44:45Z
dc.date.issued 2014-04-01
dc.identifier.bibliographicCitation Bulletin of Mathematical Sciences, 4 (1), pp. 83-97
dc.identifier.issn 1664-3607
dc.identifier.uri http://hdl.handle.net/10016/23331
dc.description.abstract We investigate algebraic and analytic properties of sequences of polynomials orthogonal with respect to the Sobolev type inner product (f.g)= ∫▒〖f(x)g(x)dμ(x)+∑_(k=1)^K▒∑_(i=0)^(N_k)▒M_█(k.i@) 〗 f^((i) ) (b_k ) g^i (b_k ) where μ is a finite positive Borel measure belonging to the Nevai class, the mass points bk are located outside the support of μ, and Mk,i are complex numbers such that Mk,Nk = 0. First, we study the existence as well as recurrence relations for such polynomials. When the values Mk,i are nonnegative real numbers, we can deduce the coefficients of the recurrence relation in terms of the connection coefficients for the sequences of polynomials orthogonal with respect to the Sobolev type inner product and those orthogonal with respect to the measure μ. The matrix of a symmetric multiplication operator in terms of the above sequence of Sobolev type orthogonal polynomials is obtained from the Jacobi matrix associated with the measure μ. Finally, we focus our attention on some outer relative asymptotics of such polynomials, which are deduced by using the above connection formulas
dc.description.sponsorship The second authorwas partially supported by the Research Fellowship Program from Ministerio de Ciencia e Innovación (MTM 2009-12740-C03-01), Spain. The first, second and third authors were partially supported by a grant from Ministerio de Economía y Competitividad. Dirección General de Investigación Científica y Técnica (MTM 2012-36732-C03-01), Spain
dc.format.extent 15
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Springer
dc.rights © The Author(s) 2013. This article is published with open access at SpringerLink.com
dc.rights Atribución 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by/3.0/es/
dc.subject.other Nevai class
dc.subject.other Sobolev inner products
dc.subject.other Orthogonal polynomials
dc.subject.other Recurrence relations
dc.subject.other Connection coefficients
dc.subject.other Outer relative asymptotics
dc.title Recurrence relations and outer relative asymptotics of orthogonal polynomials with respect to a discrete Sobolev type inner product
dc.type article
dc.relation.publisherversion http://dx.doi.org/10.1007/s13373-013-0047-x
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1007/s13373-013-0047-x
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2009-12740-C03-01
dc.relation.projectID Gobierno de España. MTM2012-36732-C03-01
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 83
dc.identifier.publicationissue 1
dc.identifier.publicationlastpage 97
dc.identifier.publicationtitle Bulletin of mathematical sciences
dc.identifier.publicationvolume 4
dc.identifier.uxxi AR/0000015451
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