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Asymptotics of derivatives of orthogonal polynomials on the real line

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Abstract

We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L 2 norm.

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Authors and Affiliations

  1. Department of Mathematics, Mathematics Department, The Open University of Israel, P.O. Box 808, Raanana, 43107, Israel

    D. S. Lubinsky

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    E. Levin & D. S. Lubinsky

Authors
  1. E. Levin
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  2. D. S. Lubinsky
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Additional information

Research supported by NSF grant DMS0400446 and US-Israel BSF grant 2004353.

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Levin, E., Lubinsky, D.S. Asymptotics of derivatives of orthogonal polynomials on the real line. Acta Math Hung 118, 115–127 (2008). https://doi.org/10.1007/s10474-007-6183-6

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  • DOI: https://doi.org/10.1007/s10474-007-6183-6

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