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Mat. Zametki, 1970, Volume 8, Issue 5, Pages 619–623 (Mi mz7009)  

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

Quasiconvex 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 quasiconvex sequencelambda $\{\lambda_\nu\}$ of convergence factors transforms Fourier series of functions whose moduli of continuity do not exceed a given modulus of continuity $\omega(\delta)$ into uniformly convergent series if and only iflambda $\lambda_n\omega(1/n)\log n\to0$. The sufficiency of this condition is already known.

Full text: PDF file (327 kB)

English version:
Mathematical Notes, 1970, 8:5, 817–819

Bibliographic databases:

UDC: 517.5
Received: 25.12.1969

Citation: S. A. Telyakovskii, “Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity”, Mat. Zametki, 8:5 (1970), 619–623; Math. Notes, 8:5 (1970), 817–819

Citation in format AMSBIB
\Bibitem{Tel70}
\by S.~A.~Telyakovskii
\paper Quasiconvex uniform-convergence factors for Fourier series of functions with a~given modulus of continuity
\jour Mat. Zametki
\yr 1970
\vol 8
\issue 5
\pages 619--623
\mathnet{http://mi.mathnet.ru/mz7009}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=279517}
\zmath{https://zbmath.org/?q=an:0216.39103|0206.35102}
\transl
\jour Math. Notes
\yr 1970
\vol 8
\issue 5
\pages 817--819
\crossref{https://doi.org/10.1007/BF01146938}


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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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