Two variable orthogonal polynomials and structured matrices

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Show simple item record Delgado, Antonia M. Geronimo, Jeffrey S. Iliev, Plamen Marcellán Español, Francisco José 2009-12-03T17:55:02Z 2009-12-03T17:55:02Z 2006
dc.identifier.bibliographicCitation SIAM Journal on Matrix Analysis and Applications, 2006, vol. 28, n. 1, p. 118-147
dc.identifier.issn 0895-4798 (Print)
dc.identifier.issn 1095-7162 (Online)
dc.description 30 pages, no figures.-- MSC2000 codes: 42C05, 30E05, 47A57.
dc.description MR#: MR2218946 (2006m:47021)
dc.description Zbl#: Zbl 1136.42305
dc.description.abstract We consider bivariate real valued polynomials orthogonal with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between polynomials of different degrees. These formulas link the orthogonal polynomials constructed using the lexicographical ordering with those constructed using the reverse lexicographical ordering. Relations between the coefficients in the recurrence formulas are established and used to give necessary and sufficient conditions for the existence of a positive linear functional. Links to the theory of matrix orthogonal polynomials are developed as well the consequences of a zero assumption on one of the coefficients in the the recurrence formulas.
dc.description.sponsorship The second and fourth authors were partially supported by NATO grant PST.CLG.979738. The second author was partially supported by an NSF grant. The first and fourth authors were partially supported by grant BFM2003-06335-C03-02 from the Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics (SIAM)
dc.rights © Society for Industrial and Applied Mathematics (SIAM)
dc.subject.other Bivariate orthogonal polynomials
dc.subject.other Positive linear functionals
dc.subject.other Moment problem
dc.subject.other Hankel matrices
dc.title Two variable orthogonal polynomials and structured matrices
dc.type article PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1137/05062946X
dc.rights.accessRights openAccess
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