Strong asymptotics for Jacobi polynomials with varying nonstandard parameters
| dc.creator | Kuijlaars, A. B. J. | |
| dc.creator | Martinez-Finkelshtein, A. | |
| dc.date | 2003-09-27 | |
| dc.date | 2004-01-10 | |
| dc.date.accessioned | 2026-07-07T05:01:29Z | |
| dc.date.available | 2026-07-07T05:01:29Z | |
| dc.description | Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(α_n, β_n)}$ is studied, assuming that $$ \lim_{n\to\infty} \frac{α_n}{n}=A, \qquad \lim_{n\to\infty} \frac{β_n}{n}=B, $$ 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 $Γ$ of a certain quadratic differential according to the equilibrium measure on $Γ$ in an external field. However, when either $α_n$, $β_n$ or $α_n+β_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential. | |
| dc.description | 31 pages, 12 figures. Some references added. To appear in Journal D'Analyse Mathematique | |
| dc.identifier | https://arxiv.org/abs/math/0309443 | |
| dc.identifier | http://arxiv.org/abs/math/0309443 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68691 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 33C45 | |
| dc.title | Strong asymptotics for Jacobi polynomials with varying nonstandard parameters | |
| dc.type | text |