2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70992Let p(t) be a trigonometric polynomial, non-negative on the unit circle. We say that a measure σbelongs to a polynomial Szego class, if the logarithm of its density is summable over the circle with the weight p(t). For the associated orthogonal polynomials, we obtain pointwise asymptotics inside the unit disc. Then, we show that these asymptotics holds in L^2-sense on the unit circle. As a corollary, we get an existence of certain modified wave operators.revised versionClassical Analysis and ODEsComplex Variables47B36, 42C05text