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

• Tivadar Danka ^[1]
  1. [1] University of Szeged

     University of Szeged

     Hungría

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 7, Nº. 2, 2015, págs. 263-289
• Idioma: inglés
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• Resumen
  • español

    Christoffel function, asymptotic behavior, Jordan curve, equillibrium measure, Green’s function.

  • English

    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.