RT Journal Article
T1 Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature
A1 Deaño Cabrera, Alfredo
A1 Huybrechs, Daan
A1 Kuijlaars, Arno B.J.
AB In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral on the real axis with a high order stationary point, and their limit distribution is also analyzed. We show that the zeros accumulate along a contour in the complex plane that has the S-property in an external field. In addition, the strong asymptotics of the orthogonal polynomials is obtained by applying the nonlinear Deift--Zhou steepest descent method to the corresponding Riemann-Hilbert problem.
YR 2010
FD 2010-01
LK https://hdl.handle.net/10016/6646
UL https://hdl.handle.net/10016/6646
LA eng
NO 33 pages, 11 figures.-- Pre-print article.
NO A. Deaño acknowledges financial support from the programme of postdoctoral grants of the Spanish Ministry of Education and Science and project MTM2006-09050. D. Huybrechs is a Postdoctoral Fellow of the Research Foundation Flanders (FWO) and is supported by FWO-Flanders project G061710N. A.B.J. Kuijlaars is supported by K.U. Leuven research grant OT/08/33, FWO-Flanders project G.0427.09, by the Belgian InteruniversityAttraction Pole P06/02, by the European Science Foundation Program MISGAM, and by grant MTM2008-06689-C02-01 of the Spanish Ministry of Science and Innovation.
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RD 1 sept. 2024