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Mat. Sb. (N.S.), 1972, Volume 88(130), Number 3(7), Pages 447–469 (Mi msb3177)  

This article is cited in 5 scientific papers (total in 5 papers)

Subsequences of the Fourier sums of functions with a given modulus of continuity

K. I. Oskolkov


Abstract: It is proved that for each modulus of continuity $\omega(\delta)$ in the class $H_\omega$ there exists a function $f$ such that for any increasing sequence $\{n_i\}_{i=1}^\infty$ of natural numbers there is a point $x$ at which
\begin{gather*} \varlimsup_{t\to\infty}\frac{S_{n_i}(f,x)-f(x)}{\omega(n_i^{-1})\log{n_i}}\geqslant A>0,
\varliminf_{t\to\infty}\frac{S_{n_i}(f,x)-f(x)}{\omega (n_i^{-1})\log{n_i}} \leqslant-A<0, \end{gather*}
where $A$ is an absolute constant. Also considered is the approximation by sequences of Fourier sums of functions of bounded variation with given modulus of continuity.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 17:3, 441–465

Bibliographic databases:

UDC: 517.5
MSC: Primary 42A20; Secondary 26A15, 26A16, 26A45, 26A86
Received: 09.09.1971

Citation: K. I. Oskolkov, “Subsequences of the Fourier sums of functions with a given modulus of continuity”, Mat. Sb. (N.S.), 88(130):3(7) (1972), 447–469; Math. USSR-Sb., 17:3 (1972), 441–465

Citation in format AMSBIB
\Bibitem{Osk72}
\by K.~I.~Oskolkov
\paper Subsequences of the Fourier sums of functions with a~given modulus of continuity
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 88(130)
\issue 3(7)
\pages 447--469
\mathnet{http://mi.mathnet.ru/msb3177}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=333549}
\zmath{https://zbmath.org/?q=an:0239.42007}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 17
\issue 3
\pages 441--465
\crossref{https://doi.org/10.1070/SM1972v017n03ABEH001523}


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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. Z. A. Chanturiya, “On uniform convergence of Fourier series”, Math. USSR-Sb., 29:4 (1976), 475–495  mathnet  crossref  mathscinet  zmath  isi
    2. V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117  mathnet  crossref  mathscinet  zmath
    3. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. O. V. Davydov, “Sequences of rectangular Fourier sums of continuous functions with given majorants of the mixed moduli of smoothness”, Sb. Math., 187:7 (1996), 981–1004  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Pachulia N.L., “$(\psi, \beta)$ – proizvodnye i priblizheniya funktsii”, Doklady adygskoi (cherkesskoi) mezhdunarodnoi akademii nauk, 14:1 (2012), 66–73  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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