Upper estimates of Christoffel function on convex domains

被引：5
作者：
Prymak, A. [1 ]
机构：
[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 455卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Christoffel function; Convex domains; Algebraic polynomials; Orthogonal polynomials; Boundary effect; R-D; INEQUALITIES;
D O I：
10.1016/j.jmaa.2017.06.079
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
New upper bounds on the pointwise behavior of Christoffel function on convex domains in R-d are obtained. These estimates are established by explicitly constructing the corresponding "needle"-like algebraic polynomials having small integral norm on the domain, and are stated in terms of few easy-to-measure geometric characteristics of the location of the point of interest in the domain. Sharpness of the results is shown and examples of applications are given. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：1984 / 2000
页数：17
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