How poles of orthogonal rational functions affect their Christoffel functions

被引：2

作者：

Deckers, Karl ^{[1
]}

Lubinsky, Doron S. ^{[2
]}

机构：

[1] Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Leuven, Belgium

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

JOURNAL OF APPROXIMATION THEORY | 2012年 / 164卷 / 09期

基金：

美国国家科学基金会;

关键词：

Orthogonal rational functions; Christoffel functions;

D O I：

10.1016/j.jat.2012.05.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that even a relatively small number of poles of a sequence of orthogonal rational functions approaching the interval of orthogonality, can prevent their Christoffel functions from having the expected asymptotics. We also establish a sufficient condition on the rate for such asymptotics, provided the rate of approach of the poles is sufficiently slow. This provides a supplement to recent results of the authors where poles were assumed to stay away from the interval of orthogonality. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1184 / 1199

页数：16