Sobolev orthogonal polynomials defined via gradient on the unit ball

被引：21

作者：

Xu, Yuan ^{[1
]}

机构：

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

JOURNAL OF APPROXIMATION THEORY | 2008年 / 152卷 / 01期

基金：

美国国家科学基金会;

关键词：

Sobolev orthogonal polynomials; several variables; unit ball;

D O I：

10.1016/j.jat.2007.11.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An explicit family of polynomials on the unit ball B(d) of R(d) is constructed, so that it is an orthonormal family with respect to the inner product < f, g > = rho integral(Bd) del f(x) . del g(x) dx + L(fg), where rho > 0, del is the gradient, and L(fg) is either the inner product on the sphere S(d-1) or f(0)g(0). (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：52 / 65

页数：14

共 13 条

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[2]

Dunkl C F., 2001, Orthogonal polynomials of several variables

[3]

FORBES G, COMMUNICATION

[4]

García-Ripoll JJ, 2001, SIAM J SCI COMPUT, V23, P1315