Affiliations: Department of Mathematics, Jinan University, Guangzhou, China. E-mail: [email protected] | School of Mathematics and Statistics, Wuhan University, Wuhan, China. E-mail: [email protected]
Note: [] Corresponding author: Zhihua Du, Department of Mathematics, Jinan University, Guangzhou 510632, China. E-mail: [email protected].
Abstract: In this paper, we study the theory of orthogonal trigonometric polynomials (OTPs). We obtain asymptotics of OTPs with positive and analytic weight functions by Riemann–Hilbert approach and find that 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 algebraic and asymptotic properties of zeros for orthogonal trigonometric polynomials.
Keywords: orthogonal trigonometric polynomials, Riemann–Hilbert approach, orthogonal polynomials on the unit circle, Christoffel–Darboux, recurrence, zeros
