Show simple item record

dc.contributor.authorFoulquié Moreno, A.
dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.contributor.authorSousa, V. L.
dc.date.accessioned2012-07-31T11:43:41Z
dc.date.available2012-07-31T11:43:41Z
dc.date.issued2011
dc.identifier.urihttp://hdl.handle.net/10835/1626
dc.description.abstractWe consider the orthogonal polynomials on [−1,1] with respect to the weight where h is real analytic and strictly positive on [−1,1] and Ξ c is a step-like function: Ξ c (x)=1 for x∈[−1,0) and Ξ c (x)=c 2, c>0, for x∈[0,1]. We obtain strong uniform asymptotics of the monic orthogonal polynomials in , as well as first terms of the asymptotic expansion of the main parameters (leading coefficients of the orthonormal polynomials and the recurrence coefficients) as n→∞. In particular, we prove for w c a conjecture of A. Magnus regarding the asymptotics of the recurrence coefficients. The main focus is on the local analysis at the origin. We study the asymptotics of the Christoffel-Darboux kernel in a neighborhood of the jump and show that the zeros of the orthogonal polynomials no longer exhibit clock behavior. For the asymptotic analysis we use the steepest descent method of Deift and Zhou applied to the noncommutative Riemann-Hilbert problems characterizing the orthogonal polynomials. The local analysis at x=0 is carried out in terms of confluent hypergeometric functions. Incidentally, we establish some properties of these functions that may have an independent interest.es_ES
dc.language.isoenes_ES
dc.sourceConstructive Approximation Vol. 33, Núm. 2 (2011)es_ES
dc.subjectPolinomios ortogonaleses_ES
dc.subjectAsintóticaes_ES
dc.subjectAnálisis de Riemann-Hilbertes_ES
dc.subjectCeroses_ES
dc.subjectComportamiento locales_ES
dc.subjectFunciones hipergeométricas confluenteses_ES
dc.subjectUniversalidades_ES
dc.subjectEspacio de Brangeses_ES
dc.subjectOrthogonal polynomialses_ES
dc.subjectAsymptoticses_ES
dc.subjectRiemann-Hilbert analysises_ES
dc.subjectZeroses_ES
dc.subjectLocal behaviores_ES
dc.subjectConfluent hypergeometric functionses_ES
dc.subjectReproducing kerneles_ES
dc.subjectUniversalityes_ES
dc.subjectde Branges spaceses_ES
dc.titleAsymptotics of orthogonal polynomials for a weight with a jump on [-1; 1]es_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


Files in this item

This item appears in the following Collection(s)

Show simple item record