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

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

Authors:

E. Berriochoa A. Cachafeiro J. GarcÍa-Amor

Affiliation:

(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

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

assuming that mgr

₁ belongs to the Szeg odblac

class as well as (1–x²)^–1 isin

L¹(

₁).Mathematics Subject Classifications (2000) 33C47, 42C05.

Keywords:

orthogonal polynomials Sobolev inner products Szeg

/content/uh6th675226vk63v/xxlarge337.gif" alt=" odblac" align=" BASELINE" BORDER=" 0" >

/content/uh6th675226vk63v/xxlarge8217.gif" alt=" rsquo" align=" BASELINE" BORDER=" 0" >s theory

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