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

JOURNAL OF APPROXIMATION THEORY

卷:139

Article

Denisov, S ; Kupin, S

关键词: orthogonal polynomials;    asymptotics;    Verblunsky coefficients;    Szego condition;    polynomial Szego condition;    modified wave operators;    Hardy and Nevanlinna classes;   

DOI  :  10.1016/j.jat.2005.02.002

来源: Elsevier

【 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 integral(2 pi)(o) p(e(io)) log sigma'(ac)(e(io)) d theta > -infinity. For the associated orthogonal polynomials {phi(n)}, we obtain pointwise asymptotics inside the unit disc D. Then we show that these asymptotics hold in L-2-sense on the unit circle. As a corollary, we get an existence of certain modified wave operators. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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