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Riemann-Hilbert analysis for Jacobi polynomials orthogonal on a single contour
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 This property is no longer valid for other values of the parameters; in general, zeros are complex.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 |