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arXiv · 1709.10509

Pointwise behavior of Christoffel function on planar convex domains

A. Prymak·O. Usoltseva
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Abstract

We prove a general lower bound on Christoffel function on planar convex domains in terms of a modification of the parallel section function of the domain. For a certain class of planar convex domains, in combination with a recent general upper bound, this allows to compute the pointwise behavior of Christoffel function. We illustrate this approach for the domains $\{(x,y):|x|^α+|y|^α\le1\}$, $1<α<2$, and compute up to a constant factor the required modification of the parallel section function, and, consequently, Christoffel function at an arbitrary interior point of the domain.

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BibTeXRIS

A. Prymak, O. Usoltseva. 2017-09-29. Pointwise behavior of Christoffel function on planar convex domains. https://arxiv.org/abs/1709.10509

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