dc.contributor.author Kuijlaars, A. B. J. dc.contributor.author Martínez-Finkelshtein, Andrei dc.date.accessioned 2012-08-03T09:38:59Z dc.date.available 2012-08-03T09:38:59Z dc.date.issued 2004 dc.identifier.issn 0021-7670 dc.identifier.uri http://hdl.handle.net/10835/1638 dc.description.abstract Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$\lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B,$$ with $A$ and $B$ satisfying $A > -1$, $B>-1$, $A+B < -1$. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case the zeros distribute on the set of critical trajectories $\Gamma$ of a certain quadratic differential according to the equilibrium measure on $\Gamma$ in an external field. However, when either $\alpha_n$, $\beta_n$ or $\alpha_n+\beta_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential. es_ES dc.language.iso en es_ES dc.source Journal d'Analyse Mathematique 94, 195-234 (2004) es_ES dc.subject Análisis asintótico es_ES dc.subject Polinomios de Jacobi es_ES dc.subject Análisis de algoritmos es_ES dc.title Strong asymptotics for Jacobi polynomials with varying nonstandard parameters. 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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