Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and Relations with OPUC

2008/05/17 by Du, Jinyuan, Du, Zhihua
#42A05 (Primary) #42C05 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0805.2640

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.

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