Orthogonal polynomials with respect to the sum of an arbitrary measure and a Bernstein-Szego measure

In the present paper we study the orthogonal polynomials with respect to a measure which is the sum of a finite positive Borel measure on [0, 2 pi] and a Bernstein - Szego measure. We prove that the measure sum belongs to the Szego class and we obtain several properties about the norms of the orthogonal polynomials, as well as, about the coefficients of the expression which relates the new orthogonal polynomials with the Bernstein - Szego polynomials. When the Bernstein - Szego measure corresponds to a polynomial of degree one, we give a nice explicit algebraic expression for the new orthogonal polynomials.