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Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval

Deaño, Alfredo (2014) Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval. Journal of Approximation Theory, 186 . pp. 33-63. ISSN 0021-9045. (doi:10.1016/j.jat.2014.07.004)

Abstract

We consider polynomials p^w_n(x) that are orthogonal with respect to the oscillatory weight w(x)=exp(iwx) on [?1,1], where w>0 is a real parameter. A first analysis of p^?_n(x) for large values of w was carried out in connection with complex Gaussian quadrature rules with uniform good properties in w. In this contribution we study the existence, asymptotic behavior and asymptotic distribution of the roots of p^?_n(x) in the complex plane as n tends to infinity. The parameter w grows with n linearly. The tools used are logarithmic potential theory and the S-property, together with the Riemann--Hilbert formulation and the Deift-Zhou steepest descent method.

Item Type: Article
DOI/Identification number: 10.1016/j.jat.2014.07.004
Additional information: Full text upload in compliance with Journal
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 02 Nov 2015 11:58 UTC
Last Modified: 29 May 2019 16:14 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51343 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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