Connections between Interval and Unit Circle for Sobolev Orthogonal Polynomials. Strong Asymptotics on the Real Line期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Connections between Interval and Unit Circle for Sobolev Orthogonal Polynomials. Strong Asymptotics on the Real Line

Authors:

E Berriochoa A Cachafeiro J GarcÍa-Amor

Institution:

(1) Departamento de Matemática Aplicada I, Facultad de Ciencias, Universidad de Vigo, Ourense, Spain;(2) Departamento de Matemática Aplicada I, E.T.S. Ingenieros Industriales, Universidad de Vigo, 36280 Vigo, Spain

Abstract:

In this paper we show the connection between Sobolev orthogonal Laurent polynomials on the unit circle and Sobolev orthogonal polynomials on a bounded interval of the real line. As a consequence we deduce the strong outer asymptotics for Sobolev orthogonal polynomials with respect to the inner product

$\langle f(x),g(x)\rangle_{s_{\mu}}=\int_{-1}^{1}f(x)g(x)\,\mathrm{d}\mu _{0}(x)+\int_{-1}^{1}f'(x)g'(x)\,\mathrm{d}\mu _{1}(x),$