Asymptotics of the orthogonal polynomials for the Szegő class with a polynomial weight |
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Authors: | S Denisov S Kupin |
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Institution: | aDepartment of Mathematics 253-37, Caltech, Pasadena, CA 91125, USA;bCMI, Université de Provence, 39 Rue Joliot Curie, 13453 Marseille Cedex 13, France |
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Abstract: | Let p be a trigonometric polynomial, non-negative on the unit circle . We say that a measure σ on belongs to the polynomial Szegő class, if , σs is singular, andFor the associated orthogonal polynomials {n}, we obtain pointwise asymptotics inside the unit disc . Then we show that these asymptotics hold in L2-sense on the unit circle. As a corollary, we get an existence of certain modified wave operators. |
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Keywords: | Orthogonal polynomials Asymptotics Verblunsky coefficients Szegő condition Polynomial Szegő condition Modified wave operators Hardy and Nevanlinna classes |
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