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Mat. Zametki, 2013, Volume 94, Issue 5, Pages 745–756 (Mi mz8778)  

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

Absolute Convergence of Fourier Series of Almost-Periodic Functions

Yu. Kh. Khasanov

Russian-Tajik Slavonic University

Abstract: We present necessary and sufficient conditions for the absolute convergence of the Fourier series of almost-periodic (in the sense of Besicovitch) functions when the Fourier exponents have limit points at infinity or at zero. The structural properties of the functions are described by the modulus of continuity or the modulus of averaging of high order, depending on the behavior of the Fourier exponents. The case of uniform almost-periodic functions of bounded variation is considered.

Keywords: almost-periodic function, Fourier series, trigonometric polynomial, function of bounded variation, modulus of continuity, Parseval's inequality.

DOI: https://doi.org/10.4213/mzm8778

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English version:
Mathematical Notes, 2013, 94:5, 692–702

Bibliographic databases:

UDC: 517.5
Received: 17.03.2010
Revised: 05.12.2012

Citation: Yu. Kh. Khasanov, “Absolute Convergence of Fourier Series of Almost-Periodic Functions”, Mat. Zametki, 94:5 (2013), 745–756; Math. Notes, 94:5 (2013), 692–702

Citation in format AMSBIB
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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. Kh. Khasanov, “On absolute Cesáro summablity of Fourier series for almost-periodic functions with limiting points at zero”, Ufa Math. J., 8:4 (2016), 144–151  mathnet  crossref  isi  elib
  • Математические заметки Mathematical Notes
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