dc.contributor.author Martínez-Finkelshtein, Andrei dc.contributor.author Orive, R. dc.date.accessioned 2012-08-03T10:08:32Z dc.date.available 2012-08-03T10:08:32Z dc.date.issued 2005 dc.identifier.uri http://hdl.handle.net/10835/1641 dc.description.abstract Classical 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 This property is no longer valid for other values of the parameters; in general, zeros are complex.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.iso en es_ES dc.source Journal of approximation theory Vol. 134, nº 2 (2005) es_ES dc.subject Análisis asintótico es_ES dc.subject Ortogonalidad no hermitiana es_ES dc.subject Caracterización de Riemann-Hilbert es_ES dc.subject Asymptotic analysis es_ES dc.subject Non-hermitian orthogonality es_ES dc.subject Steepest descent method es_ES dc.subject Riemann–Hilbert characterization es_ES dc.title Riemann-Hilbert analysis for Jacobi polynomials orthogonal on a single contour es_ES dc.type info:eu-repo/semantics/article es_ES dc.rights.accessRights info:eu-repo/semantics/openAccess es_ES
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