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arXiv · 0805.2640

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

Jinyuan Du·Zhihua Du
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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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Jinyuan Du, Zhihua Du. 2008-05-17. Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and Relations with OPUC. https://arxiv.org/abs/0805.2640

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