Asymptotics of the orthogonal polynomials for the Szego class with a polynomial weight

摘要

Let P be a trigonometric polynomial, non-negative on the unit circle T. We say that a measure sigma on T belongs to the polynomial Szego class, if d sigma(e(io)) = sigma'(ac) (e(io)) d theta + d sigma(s)(e(io)), sigma(s) is singular, and