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Sbornik: Mathematics, 2014, Volume 205, Issue 11, Pages 1620–1649
DOI: https://doi.org/10.1070/SM2014v205n11ABEH004431 (Mi sm8332) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Concentration of the $L_1$-norm of trigonometric polynomials and entire functions

Yu. V. Malykhina, K. S. Ryutinb

a Steklov Mathematical Institute of Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (673 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2014v205n11ABEH004431
Abstract: For any sufficiently large $n$, the minimal measure of a subset of $[-\pi,\pi]$ on which some nonzero trigonometric polynomial of order $\le n$ gains half of the $L_1$-norm is shown to be $\pi/(n+1)$. A similar result for entire functions of exponential type is established.
Bibliography: 13 titles.
Keywords: trigonometric polynomials, entire functions, extremal problems, $L_1$-norm.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00332
Received: 21.01.2014 and 03.07.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 11, Pages 95–124
DOI: https://doi.org/10.4213/sm8332
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: 42A05
Language: English
Original paper language: Russian
Citation: Yu. V. Malykhin, K. S. Ryutin, “Concentration of the $L_1$-norm of trigonometric polynomials and entire functions”, Mat. Sb., 205:11 (2014), 95–124; Sb. Math., 205:11 (2014), 1620–1649
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2014v205n11ABEH004431
  • https://www.mathnet.ru/eng/sm/v205/i11/p95
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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