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Mat. Sb., 2014, Volume 205, Number 11, Pages 95–124 (Mi msb8332)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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


DOI: https://doi.org/10.4213/sm8332

Full text: PDF file (718 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:11, 1620–1649

Bibliographic databases:

UDC: 517.51
MSC: 42A05
Received: 21.01.2014 and 03.07.2014

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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  • http://mi.mathnet.ru/eng/msb/v205/i11/p95

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. D. Livshits, “On Uniform Approximation on Subsets”, Math. Notes, 98:5 (2015), 860–863  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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