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Mat. Zametki, 1971, Volume 10, Issue 1, Pages 33–40 (Mi mz7064)  

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

Uniform-convergence factors for Fourier series of functions with a given modulus of continuity

S. A. Telyakovskii

Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: It is proved that a sequence of factors $\{\lambda_\nu\}$, which are Fourier–Stieitjes coefficients, converts the Fourier series of any function whose modulus of continuity does not exceed a given modulus of continuity $\omega(\delta)$ into a uniformly convergent series, if and only if $\omega(1/n)\int_o^{2\pi}|\lambda_0/2+\sum_{\nu=1}^n\lambda_\nu\cos\nu t|dt=o(1)$. The sufficiency of this condition is known.

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English version:
Mathematical Notes, 1971, 10:1, 444–448

Bibliographic databases:

UDC: 517.5
Received: 08.07.1970

Citation: S. A. Telyakovskii, “Uniform-convergence factors for Fourier series of functions with a given modulus of continuity”, Mat. Zametki, 10:1 (1971), 33–40; Math. Notes, 10:1 (1971), 444–448

Citation in format AMSBIB
\Bibitem{Tel71}
\by S.~A.~Telyakovskii
\paper Uniform-convergence factors for Fourier series of functions with a~given modulus of continuity
\jour Mat. Zametki
\yr 1971
\vol 10
\issue 1
\pages 33--40
\mathnet{http://mi.mathnet.ru/mz7064}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=290023}
\zmath{https://zbmath.org/?q=an:0223.42003}
\transl
\jour Math. Notes
\yr 1971
\vol 10
\issue 1
\pages 444--448
\crossref{https://doi.org/10.1007/BF01747067}


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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. N. Yu. Agafonova, S. S. Volosivets, “Multipliers of Convergence in Norm of Series with Respect to Multiplicative Systems”, Math. Notes, 82:4 (2007), 433–442  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математические заметки Mathematical Notes
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