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Orthogonal polynomials and quadratic transformations

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorMarcellán Español, Francisco José
dc.contributor.authorPetronilho, José
dc.date.accessioned2010-01-04T12:13:17Z
dc.date.available2010-01-04T12:13:17Z
dc.date.issued1999
dc.description33 pages, no figures.-- MSC1991 code: Primary 42C05.
dc.descriptionMR#: MR1680116 (2000b:42021)
dc.descriptionZbl#: Zbl 0936.42012
dc.description.abstractStarting from a sequence $\{P_n\}_{n\geq 0}$ of monic polynomials orthogonal with respect to a linear functional ${\bf u}$, we find a linear functional ${\bf v}$ such that $\{Q_n\}_{\geq 0}$, with either $Q_{2n}(x)=P_n(T(x))$ or $Q_{2n+1}(x)=(x-a)\,P_n(T(x))$ where $T$ is a monic quadratic polynomial and $a\in\C$, is a sequence of monic orthogonal polynomials with respect to ${\bf v}$. In particular, we discuss the case when ${\bf u}$ and ${\bf v}$ are both positive definite linear functionals. Thus, we obtain a solution for an inverse problem which is a converse, for quadratic mappings, of one analyzed in [11].
dc.description.sponsorshipThis paper was finished with financial support of a Grant from Junta Nacional de Investigação Científica e Tecnológica (JNITC) - BD976 - and Centro de Matemática da Universidade de Coimbra (CMUC) of Portugal. The work of the first author was supported by the Dirección General de Enseñanza Superior (DGES) of Spain - PB96-0120-C03-01.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationPortugaliae Mathematica, 1999, vol. 56, n. 1, p. 81-113
dc.identifier.issn0032-5155
dc.identifier.urihttps://hdl.handle.net/10016/6263
dc.language.isoeng
dc.publisherEuropean Mathematical Society
dc.relation.publisherversionhttp://www.emis.de/journals/PM/56f1/5.html
dc.rights© European Mathematical Society
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherOrthogonal polynomials
dc.subject.otherRecurrence coefficients
dc.subject.otherPolynomial mappings
dc.subject.otherStieltjes functions
dc.titleOrthogonal polynomials and quadratic transformations
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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