Christoffel function on planar domains with piecewise smooth boundary

TL;DR

This paper derives a formula for the Christoffel function on certain planar domains with piecewise smooth boundaries, relating it to distances from the point to boundary curves, useful for approximation theory.

Contribution

It provides an explicit computation of the Christoffel function on domains with piecewise smooth boundary, including corner points with angles between 0 and π.

Findings

Formula relates Christoffel function to boundary distances

Applicable to domains with finitely many $C^2$ boundary curves

Handles corners with interior angles between 0 and π

Abstract

We compute up to a constant factor the Christoffel function on planar domains with boundary consisting of finitely many $C^2$ curves such that each corner point of the boundary has interior angle strictly between $0$ and $\pi$. The resulting formula uses the distances from the point of interest to the curves or certain parts of the curves defining the boundary of the domain.