Skip to main content

Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature

Deaño, Alfredo, Huybrechs, Daan, Kuijlaars, Arno B. J. (2010) Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature. Journal of Approximation Theory, 162 . pp. 2202-2224. ISSN 0021-9045. (doi:10.1016/j.jat.2010.07.006) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1016/j.jat.2010.07.006

Abstract

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 are obtained by applying the nonlinear Deift-Zhou steepest descent method to the corresponding Riemann-Hilbert problem.

Item Type: Article
DOI/Identification number: 10.1016/j.jat.2010.07.006
Uncontrolled keywords: Oscillatory integralsGaussian quadratureSteepest descent methodComplex orthogonal polynomialsRiemann–Hilbert analysis
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 20 Nov 2018 18:10 UTC
Last Modified: 30 May 2019 08:21 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70217 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
  • Depositors only (login required):