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

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

2008-05-17

arxiv.org/abs/0805.2640v1

Physics

Mathematical Physics

38 pages

Scientific paper

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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