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dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.contributor.authorOrive, R.
dc.date.accessioned2012-08-03T10:08:32Z
dc.date.available2012-08-03T10:08:32Z
dc.date.issued2005
dc.identifier.urihttp://hdl.handle.net/10835/1641
dc.description.abstractClassical Jacobi polynomials $P_{n}^{(\alpha,\beta)}$, with $\alpha, \beta>-1$, have a number of well-known properties, in particular the location of their zeros in the open interval $(-1,1)$. This property is no longer valid for other values of the parameters; in general, zeros are complex. In this paper we study the strong asymptotics of Jacobi polynomials where the real parameters $\alpha_n,\beta_n$ depend on $n$ in such a way that $$ \lim_{n\to\infty}\frac{\alpha_{n}}{n}=A, \quad \lim_{n\to\infty}\frac{\beta_{n}}{n}=B, $$ with $A,B \in \mathbb{R}$. We restrict our attention to the case where the limits $A,B$ are not both positive and take values outside of the triangle bounded by the straight lines A=0, B=0 and $A+B+2=0$. As a corollary, we show that in the limit the zeros distribute along certain curves that constitute trajectories of a quadratic differential. The non-hermitian orthogonality relations for Jacobi polynomials with varying parameters lie in the core of our approach; in the cases we consider, these relations hold on a single contour of the complex plane. The asymptotic analysis is performed using the Deift-Zhou steepest descent method based on the Riemann-Hilbert reformulation of Jacobi polynomials.es_ES
dc.language.isoenes_ES
dc.sourceJournal of approximation theory Vol. 134, nº 2 (2005)es_ES
dc.subjectAnálisis asintóticoes_ES
dc.subjectOrtogonalidad no hermitianaes_ES
dc.subjectCaracterización de Riemann-Hilbertes_ES
dc.subjectAsymptotic analysises_ES
dc.subjectNon-hermitian orthogonalityes_ES
dc.subjectSteepest descent methodes_ES
dc.subjectRiemann–Hilbert characterizationes_ES
dc.titleRiemann-Hilbert analysis for Jacobi polynomials orthogonal on a single contoures_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


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