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

2015/04/23 by Tivadar Danka, Danka, Tivadar
Mathematics · #31A99 #42C05 #Analytic Number Theory Research #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #math.CA #msc:31A99 #msc:42C05

paper · pdf · doi:10.48550/arxiv.1504.06245

20 pages

arxiv created 2015/04/23 · openalex publication_date 2015/04/23 · arxiv updated 2015/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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