Orthogonal trigonometric polynomials from Riemann-Hilbert view
arXiv:2112.07851
Abstract
In this work, some theorems are established for orthogonal trigonometric polynomials (OTP) including Favard, Baxter, Geronimus, Rakhmanov, Szegö and the strong Szegö theorems which are important in the theory of orthogonal polynomials on the unit circle (OPUC). All these results are based on the mutual representation theorem of OPUC and OTP which deduced by a Riemann-Hilbert problem simultaneously characterizing them. In addition, Szegö recursions, four-term recurrences and some new identities for OPUC and OTP are also obtained by using their Riemann-Hilbert characterizations respectively.
32 pages. arXiv admin note: text overlap with arXiv:0807.3712