Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and the strong Szeg\"o theorems for orthogonal trigonometric polynomials

Abstract

In this paper, we obtain some analogs of Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and the strong Szeg\"o theorems appeared in the theory of orthogonal polynomials on the unit circle (OPUC) for orthogonal trigonometric polynomials (OTP). The key tool is the mutual representation theorem for OPUC and OTP.