dc.creator | Arvesú Carballo, Jorge | es |
dc.creator | Marcellán Español, Francisco | es |
dc.creator | Álvarez Nodarse, Renato | es |
dc.date.accessioned | 2016-07-21T09:16:26Z | |
dc.date.available | 2016-07-21T09:16:26Z | |
dc.date.issued | 2002-04 | |
dc.identifier.citation | Arvesú Carballo, J., Marcellán Español, F. y Álvarez Nodarse, R. (2002). On a modification of the Jacobi linear functional asymptotic properties and zeros of the corresponding orthogonal polynomials. Acta Applicandae Mathematica, 71 (2), 127-158. | |
dc.identifier.issn | 0167-8019 | es |
dc.identifier.issn | 1572-9036 | es |
dc.identifier.uri | http://hdl.handle.net/11441/43837 | |
dc.description.abstract | The paper deals with orthogonal polynomials in the case where the orthogonality condition is related to semiclassical functionals. The polynomials that we discuss are a generalization of Jacobi polynomials and Jacobi-type polynomials. More precisely, we study some algebraic properties
as well as the asymptotic behaviour of polynomials orthogonal with respect to the linear functional U
U = Jα,β + A1δ(x − 1) + B1δ(x + 1) − A2δ
(x − 1) − B2δ
(x + 1),
where Jα,β is the Jacobi linear functional, i.e.
Jα,β , p = 1
−1
p(x)(1 − x)α(1 + x)β dx, α, β > −1, p ∈ P,
and P is the linear space of polynomials with complex coefficients. The asymptotic properties are analyzed in (−1, 1) (inner asymptotics) and C \ [−1, 1] (outer asymptotics) with respect to the behaviour of Jacobi polynomials. In a second step, we use the above results in order to obtain the location of zeros of such orthogonal polynomials. Notice that the linear functional U is a generalization of one studied by T. H. Koornwinder when A2 = B2 = 0. From the point of view of rational approximation, the corresponding Markov function is a perturbation of the Jacobi–Markov
function by a rational function with two double poles at ±1. The denominators of the [n−1/n] Padé approximants are our orthogonal polynomials. | es |
dc.description.sponsorship | Dirección General de Investigación | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Springer | es |
dc.relation.ispartof | Acta Applicandae Mathematica, 71 (2), 127-158. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Semiclassical orthogonal polynomials | es |
dc.subject | Asymptotics | es |
dc.subject | Zeros | es |
dc.title | On a modification of the Jacobi linear functional asymptotic properties and zeros of the corresponding orthogonal polynomials | es |
dc.type | info:eu-repo/semantics/article | es |
dc.type.version | info:eu-repo/semantics/acceptedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | BFM2000-0029 | es |
dc.relation.projectID | BFM2000-0206-C04-01 | es |
dc.relation.projectID | BFM2000-0206-C04-02 | es |
dc.relation.publisherversion | http://dx.doi.org/10.1023/A:1014510004699 | es |
dc.identifier.doi | 10.1023/A:1014510004699 | es |
dc.contributor.group | Universidad de Sevilla. FQM262: Teoria de la Aproximacion | es |
idus.format.extent | 32 p. | es |
dc.journaltitle | Acta Applicandae Mathematica | es |
dc.publication.volumen | 71 | es |
dc.publication.issue | 2 | es |
dc.publication.initialPage | 127 | es |
dc.publication.endPage | 158 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/43837 | |
dc.contributor.funder | Dirección General de Enseñanza Superior. España | |