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Bernstein’s Problem on Weighted Polynomial Approximation

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Operator-Related Function Theory and Time-Frequency Analysis

Part of the book series: Abel Symposia ((ABEL,volume 9))

Abstract

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein’s weighted uniform norm. Equivalently, for a positive finite measure μ on the real line we give a criterion for density of polynomials in L p(μ).

The author is supported by N.S.F. grant DMS-1101278.

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Acknowledgements

I am grateful to Nikolai Makarov and Misha Sodin for introducing me to the general area of Bernstein’s problem and for valuable discussions.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Alexei Poltoratski

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  1. Alexei Poltoratski
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Correspondence to Alexei Poltoratski .

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Editors and Affiliations

  1. University of Vienna, Faculty of Mathematics, Vienna, Austria

    Karlheinz Gröchenig

  2. Norwegian University of Science and Technology, Dept of Mathematical Sciences, Trondheim, Norway

    Yurii Lyubarskii

  3. Norwegian University of Science and Technology, Dept of Mathematical Sciences, Trondheim, Norway

    Kristian Seip

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Poltoratski, A. (2015). Bernstein’s Problem on Weighted Polynomial Approximation. In: Gröchenig, K., Lyubarskii, Y., Seip, K. (eds) Operator-Related Function Theory and Time-Frequency Analysis. Abel Symposia, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-08557-9_6

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