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A Problem of Totik on Fast Decreasing Polynomials

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Constructive Approximation Aims and scope

Abstract.

We solve a problem posed by V. Totik on the existence of fast-decreasing polynomials p n of degree \(\leq n\) with p n (0)=1 and \(|p_n(x)|\leq C\exp(-cn|x|^\beta)\) for \(x \in [-1,1]\) . For \(0 \leq \beta \leq 2\) the largest c for which such polynomials exist was known. We give the solution for β > 2 .

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Authors and Affiliations

  1. Faculteit Wiskunde en Informatica Universiteit van Amsterdam Plantage Muidergracht 24 NL-1018 TV Amsterdam The Netherlands , NL

    A. B. J. Kuijlaars

  2. W. Van Assche Departement Wiskunde Katholieke Universiteit Leuven Celestijnenlaan 200 B B-3001 Heverlee (Leuven) Belgium , BE

    W. Van Assche

Authors
  1. A. B. J. Kuijlaars
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  2. W. Van Assche
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April 18, 1996.

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Kuijlaars, A., Van Assche, W. A Problem of Totik on Fast Decreasing Polynomials. Constr. Approx. 14, 97–112 (1998). https://doi.org/10.1007/s003659900065

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  • DOI: https://doi.org/10.1007/s003659900065

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