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Strong asymptotics for Jacobi polynomials with varying nonstandard parameters.
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 |