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Sbornik: Mathematics, 2012, Volume 203, Issue 12, Pages 1736–1760
DOI: https://doi.org/10.1070/SM2012v203n12ABEH004285 (Mi sm8176) 		 
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
English version PDF (406 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2012v203n12ABEH004285
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.
Received: 27.08.2012
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 12, Pages 57–80
DOI: https://doi.org/10.4213/sm8176
Bibliographic databases:
Document Type: Article
UDC: 517.537.72+511.332
MSC: 30B50, 41A46
Language: English
Original paper language: Russian
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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  • https://www.mathnet.ru/eng/sm/v203/i12/p57
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:252
    English version PDF:12
    References:98
    First page:76
     
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