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

Loading...
Thumbnail Image
Identifiers
Publication date
2014-10
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
We consider polynomials pω n (x) that are orthogonal with respect to the oscillatory weight w(x) = eiωx on [−1, 1], where ω > 0 is a real parameter. A first analysis of pω n (x) for large values of ω was carried out in Asheim et al. (2014), in connection with complex Gaussian quadrature rules with uniform good properties in ω. In this contribution we study the existence, asymptotic behavior and asymptotic distribution of the roots of pω n (x) in the complex plane as n → ∞. The parameter ω 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.
Description
Keywords
Orthogonal polynomials in the complex plane, Strong asymptotics, Zero distribution, Logarithmic potential theory, S-property, Steepest descent method, Riemann-Hilbert problem
Bibliographic citation
Journal of Approximation Theory, October 2014, Vol.186, October 2014, pp. 33–63