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Extensions of Bernstein’s Lethargy Theorem

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Algebra, Complex Analysis, and Pluripotential Theory (USUZCAMP 2017)

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Abstract

In this paper, we examine the aptly-named “Lethargy Theorem” of Bernstein and survey its recent extensions. We show that one of these extensions shrinks the interval for best approximation by half while the other gives a surprising connection to the space of bounded linear operators between two Banach spaces.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Claremont McKenna College, Claremont, CA, 91711, USA

    Asuman Güven Aksoy

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  1. Asuman Güven Aksoy
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Correspondence to Asuman Güven Aksoy .

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Editors and Affiliations

  1. Department of Mathematics, California State University, Fullerton, CA, USA

    Zair Ibragimov

  2. Department of Mathematics, Indiana University, Bloomington, IN, USA

    Norman Levenberg

  3. Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

    Utkir Rozikov

  4. Department of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

    Azimbay Sadullaev

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Aksoy, A.G. (2018). Extensions of Bernstein’s Lethargy Theorem. In: Ibragimov, Z., Levenberg, N., Rozikov, U., Sadullaev, A. (eds) Algebra, Complex Analysis, and Pluripotential Theory. USUZCAMP 2017. Springer Proceedings in Mathematics & Statistics, vol 264. Springer, Cham. https://doi.org/10.1007/978-3-030-01144-4_2

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