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arXiv · 1704.03025

Upper estimates of Christoffel function on convex domains

A. Prymak
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Abstract

New upper bounds on the pointwise behaviour of Christoffel function on convex domains in ${\mathbb{R}}^d$ 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.

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BibTeXRIS

A. Prymak. 2017-06-30. Upper estimates of Christoffel function on convex domains. https://doi.org/10.1016/j.jmaa.2017.06.079

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