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

Connections between Interval and Unit Circle for Sobolev Orthogonal Polynomials. Strong... 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 $$\langle f(x),g(x)\rangle_{s_{\mu}}=\int_{-1}^{1}f(x)g(x)\,\mathrm{d}\mu _{0}(x)+\int_{-1}^{1}f'(x)g'(x)\,\mathrm{d}\mu _{1}(x),$$ assuming that μ1 belongs to the Szegő class as well as (1−x 2)−1∈L 1(μ1). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

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

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References (12)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-004-7025-y
Publisher site
See Article on Publisher Site

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 $$\langle f(x),g(x)\rangle_{s_{\mu}}=\int_{-1}^{1}f(x)g(x)\,\mathrm{d}\mu _{0}(x)+\int_{-1}^{1}f'(x)g'(x)\,\mathrm{d}\mu _{1}(x),$$ assuming that μ1 belongs to the Szegő class as well as (1−x 2)−1∈L 1(μ1).

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 1, 2004

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