Differential properties for a class of Sobolev orthogonal polynomials

被引：0

作者：

Berriochoa, E ^{[1
]}

Cachafeiro, A ^{[1
]}

机构：

[1] Univ Vigo, Dept Matemat Aplicada, ETSI Ind, Vigo 36280, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2002年 / 146卷 / 02期

关键词：

orthogonal polynomials; minimal norm; recurrence relation; asymptotics; differential equation;

D O I：

10.1016/S0377-0427(02)00369-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the orthogonal polynomials with respect to a Sobolev inner product of the following type: (f,g)(s) = integral(0)(2pi) f(e(10))g(e(10))\B-h(e(10))\(2) dtheta/2pi + 1/lambda integral(0)(2pi) f'(e(10))g(t)(e(10))dtheta/2pidegrees z = e(10), where B-h(z) is a complex polynomial of degree h, dtheta/2pi is the normalized Lebesgue measure and lambda is a positive real number. The asymptotic behavior in the complex plane, as well as the differential equations satisfied by the orthogonal polynomials are obtained. As an application, two differential problems are solved, one of them is like a Dirichlet boundary value problem. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：361 / 372

页数：12