Journal
JOURNAL OF APPROXIMATION THEORY
Volume 268, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jat.2021.105603
Keywords
Christoffel function; Algebraic polynomials; Orthogonal polynomials; Boundary effect
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Funding
- Natural Sciences and Engineering Research Council of Canada [RGPIN 05357-20]
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The paper computes the behavior of the Christoffel function in an arbitrary planar convex domain up to a constant factor, using comparison with other simple reference domains. By constructing appropriate ellipse and parallelogram containing the domain, lower and upper bounds are obtained respectively. As an application, a new proof is presented that every planar convex domain possesses optimal polynomial meshes.
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.
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