Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach
type: CreativeWork
description: We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow the steepest descent method of matrix transformations developed by Deift and Zhou.
abstract: We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow the steepest descent method of matrix transformations developed by Deift and Zhou.
author: Naugle, Lynsey Cargile
keywords: Mathematics
date published: 2017-01-01T08:00:00Z
date modified: 2026-07-24T03:05:53Z
provider: University of Mississippi
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Mississippi