Upper estimates of Christoffel function on convex domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Prymak, A.¹ 

[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

关键词: Christoffel function;    Convex domains;    Algebraic polynomials;    Orthogonal polynomials;    Boundary effect;   

DOI  :  10.1016/j.jmaa.2017.06.079

来源: Elsevier

【 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.

【 授权许可】

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