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Asymptotics for Christoffel functions for general measures on the real line

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Abstract

We consider asymptotics of Christoffel functions for measures ν with compact support on the real line. It is shown that under some natural conditionsn times thenth Christoffel function has a limit asn→∞ almost everywhere on the support, and the limit is the Radon-Nikodym derivative of ν with respect to the equilibrium measure of the support of ν. The case in which the support is an interval was settled previously by A. Máté, P. Nevai and the author. The present paper solves the general problem.

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Authors and Affiliations

  1. Bolyai Institute, Aradi V. Tere 1, 6720, Szeged, Hungary

    Vilmos Totik

  2. Department of Mathematics, University of South Florida, 33620, Tampa, FL, USA

    Vilmos Totik

Authors
  1. Vilmos Totik
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Additional information

Work was supported by the National Science Foundation, DMS 9801435 and by the Hungarian National Science Foundation for Research, T/022983.

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Totik, V. Asymptotics for Christoffel functions for general measures on the real line. J. Anal. Math. 81, 283–303 (2000). https://doi.org/10.1007/BF02788993

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  • DOI: https://doi.org/10.1007/BF02788993

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