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

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.

20 pages