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

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

2004-04-28

arxiv.org/abs/math/0404506v2

Mathematics

Classical Analysis and ODEs

revised version

Scientific paper

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.

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