A family of Sobolev orthogonal polynomials on the unit circle

被引：5

作者：

Berriochoa, E

Cachafeiro, A

机构：

[1] Univ Vigo, Fac Ciencias, Dept Matemat Aplicada, Vigo, Spain

[2] Univ Vigo, ETSII, Dept Matemat Aplicada, Vigo, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1999年 / 105卷 / 1-2期

关键词：

orthogonal polynomial; Sobolev inner product; measure on the unit circle;

D O I：

10.1016/S0377-0427(99)00040-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to study the polynomials orthogonal with respect to the following Sobolev inner product: [P, Q](s1) = integral(0)(2 pi) P(e(i theta))<(Q(e(i theta)))over bar>d mu(theta) + 1/lambda integral(0)(2 pi) P'(e(i theta))<(Q'(e(i theta)))over bar>d nu(theta), z = e(i theta), lambda = 0, where nu is the normalized Lebesgue measure and mu is a rational modification of nu. In this situation we analyse the algebraic results and the asymptotic behaviour of such orthogonal polynomials. Moreover some properties about the distribution of their zeros are given. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：163 / 173

页数：11

共 9 条

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BREZIS H, 1984, ANAL FUCNTIONAL ALIA

[2] ORTHOGONAL POLYNOMIALS OF SOBOLEV TYPE ON THE UNIT-CIRCLE [J].