Geometric computation of Christoffel functions on planar convex domains

JOURNAL OF APPROXIMATION THEORY

卷:268

Article

Prymak, A.¹ 

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

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

DOI  :  10.1016/j.jat.2021.105603

来源: Elsevier

【 摘 要 】

For an arbitrary planar convex domain, we compute the behavior of Christoffel function up to a constant factor using comparison with other simple reference domains. The lower bound is obtained by constructing an appropriate ellipse contained in the domain, while for the upper bound an appropriate parallelogram containing the domain is constructed. As an application we obtain a new proof that every planar convex domain possesses optimal polynomial meshes. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free