Christoffel functions on Jordan curves with respect to measures with jump singularity

TL;DR

This paper investigates the asymptotic behavior of Christoffel functions on Jordan curves with measures exhibiting jump singularities, extending known results from intervals to more complex sets using polynomial inverse images.

Contribution

It introduces new asymptotic results for Christoffel functions on Jordan curves with singular measures, generalizing previous interval-based findings through polynomial inverse images.

Findings

Asymptotic limits expressed via equilibrium measure or Green's function

Extension of results from intervals to Jordan curves

Handling measures with jump singularities

Abstract

In this paper we establish asymptotic results for Christoffel functions with respect to measures supported on Jordan curves having a Radon-Nikodym derivative with a jump singularity. We extend the results known for measures supported in the interval $ [-1,1] $ to more general sets, for example a system of Jordan curves, using polynomial inverse images. It is shown that the asymptotic limit can be written in terms of the equilibrium measure or Green's function.