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dc.contributor.authorKuijlaars, A. B. J.
dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.date.accessioned2012-08-03T09:38:59Z
dc.date.available2012-08-03T09:38:59Z
dc.date.issued2004
dc.identifier.issn0021-7670
dc.identifier.urihttp://hdl.handle.net/10835/1638
dc.description.abstractStrong 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.isoenes_ES
dc.sourceJournal d'Analyse Mathematique 94, 195-234 (2004)es_ES
dc.subjectAnálisis asintóticoes_ES
dc.subjectPolinomios de Jacobies_ES
dc.subjectAnálisis de algoritmoses_ES
dc.titleStrong asymptotics for Jacobi polynomials with varying nonstandard parameters.es_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


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