Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and   Relations with OPUC
  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. 
Jinyuan Du, Zhihua Du