  Let p(t) be a trigonometric polynomial, non-negative on the unit circle. We
say that a measure \sigma belongs 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.

Classical Analysis and ODEs;Complex Variables