About semiclassical polynomials on the unit circle corresponding to the class (2,2)

In the present paper we pose the problem of characterizing the orthogonal polynomials related to the unit circle whose moment functional L verify a functional relation of the following type D(φL) + ψL = 0, where φ and ψ are polynomials with deg φ = 2 and deg ψ = 1. Two different situations appear depending on whether the roots of φ are unimodular or not. Here, we solve the last case. Moreover, we analyse the definite positive character of the solutions.