Journal d’Analyse Mathématique

, Volume 81, Issue 1, pp 283–303

Asymptotics for Christoffel functions for general measures on the real line


  • Vilmos Totik
    • Bolyai Institute
    • Department of MathematicsUniversity of South Florida

DOI: 10.1007/BF02788993

Cite this article as:
Totik, V. J. Anal. Math. (2000) 81: 283. doi:10.1007/BF02788993


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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© Hebrew University of Jerusalem 2000