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Mat. Zametki, 2007, Volume 81, Issue 5, Pages 707–712 (Mi mz3714)  

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

Completeness of the Trigonometric System for the Classes $\varphi(L)$

Yu. S. Kolomoitsev

Donetsk National University

Abstract: We obtain a necessary and sufficient condition for the completeness of the trigonometric system with gaps for the classes $\varphi(L)$.

Keywords: trigonometric system with gaps, $2\pi$-periodic function, Jensen's inequality, trigonometric polynomial, Parseval's equality, Riesz–Fischer theorem

DOI: https://doi.org/10.4213/mzm3714

Full text: PDF file (461 kB)
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English version:
Mathematical Notes, 2007, 81:5, 632–637

Bibliographic databases:

UDC: 517.5
Received: 24.01.2006
Revised: 05.10.2006

Citation: Yu. S. Kolomoitsev, “Completeness of the Trigonometric System for the Classes $\varphi(L)$”, Mat. Zametki, 81:5 (2007), 707–712; Math. Notes, 81:5 (2007), 632–637

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm3714
  • http://mi.mathnet.ru/eng/mz/v81/i5/p707

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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. Yu. S. Kolomoitsev, “On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0<p<1$”, J. Math. Sci. (N. Y.), 165:4 (2010), 463–472  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
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