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Oscillatory behavior of orthogonal polynomials

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Abstract

It is shown that under fairly weak conditions on the measure the orthonormal polynomials have almost everywhere oscillatory behavior. A simple lower bound for the amplitude of oscillation is also given in terms of the measure and the equilibrium density of the support. This bound is also shown to be exact in some situations.

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Authors and Affiliations

  1. MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Aradi v. tere 1, 6720, Szeged, Hungary

    V. Totik

  2. Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave, CMC342, Tampa, FL, 33620-5700, USA

    V. Totik

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  1. V. Totik
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Correspondence to V. Totik.

Additional information

Dedicated to Zoltán Daróczy, for a long and amiable relationship

Supported by NSF DMS 1564541.

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Totik, V. Oscillatory behavior of orthogonal polynomials. Acta Math. Hungar. 160, 453–467 (2020). https://doi.org/10.1007/s10474-019-00990-x

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  • DOI: https://doi.org/10.1007/s10474-019-00990-x

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