Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and Relations with OPUC
Mathematical Physics
2008-05-20 v1 Complex Variables
math.MP
Abstract
In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials on the unit circle (OPUC). By the relations and the theory of OPUC, we also get four-terms recurrent formulae, Christoffel-Darboux formula and some properties of zeros for orthogonal trigonometric polynomials.
Cite
@article{arxiv.0805.2640,
title = {Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and Relations with OPUC},
author = {Jinyuan Du and Zhihua Du},
journal= {arXiv preprint arXiv:0805.2640},
year = {2008}
}
Comments
38 pages