Geometric computation of Christoffel functions on planar convex domains
Classical Analysis and ODEs
2021-06-16 v3
Abstract
For 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 parallelepiped containing the domain is constructed. As an application we obtain a new proof of existence of optimal polynomial meshes in planar convex domains.
Keywords
Cite
@article{arxiv.2003.12833,
title = {Geometric computation of Christoffel functions on planar convex domains},
author = {A. Prymak},
journal= {arXiv preprint arXiv:2003.12833},
year = {2021}
}