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Mat. Sb., 2012, Volume 203, Number 12, Pages 57–80 (Mi msb8176)  

This article is cited in 2 scientific papers (total in 2 papers)

Uniform approximation of partial sums of a Dirichlet series by shorter sums and $\Phi$-widths

J. Bourgaina, B. S. Kashinb

a Institute for Advanced Study, Princeton, NJ
b Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: It is shown that each Dirichlet polynomial $P$ of degree $N$ which is bounded in a certain natural Euclidean norm, admits a nontrivial uniform approximation on the corresponding interval on the real axis by a Dirichlet polynomial with spectrum containing significantly fewer than $N$ elements. Moreover, this spectrum is independent of $P$.
Bibliography: 19 titles.

Keywords: Dirichlet series, widths, $\varepsilon$-entropy.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8176

Full text: PDF file (623 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:12, 1736–1760

Bibliographic databases:

UDC: 517.537.72+511.332
MSC: 30B50, 41A46
Received: 27.08.2012

Citation: J. Bourgain, B. S. Kashin, “Uniform approximation of partial sums of a Dirichlet series by shorter sums and $\Phi$-widths”, Mat. Sb., 203:12 (2012), 57–80; Sb. Math., 203:12 (2012), 1736–1760

Citation in format AMSBIB
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\by J.~Bourgain, B.~S.~Kashin
\paper Uniform approximation of partial sums of a~Dirichlet series by shorter sums and $\Phi$-widths
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\pages 57--80
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\yr 2012
\vol 203
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  • http://mi.mathnet.ru/eng/msb8176
  • https://doi.org/10.4213/sm8176
  • http://mi.mathnet.ru/eng/msb/v203/i12/p57

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Pernai, “Spaces Generated by the Generalized Majorant of Partial Sums”, Math. Notes, 96:1 (2014), 154–157  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Roy A., Vatwani A., “Zeros of Partial Sums of l-Functions”, Adv. Math., 346 (2019), 467–509  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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