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Mat. Zametki, 1970, Volume 7, Issue 1, Pages 7–18 (Mi mz6988)  

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

Unbounded divergence of Fourier series of continuous functions

V. V. Buzdalin

Patrice Lumumba Peoples Friendship University

Abstract: For any given set $E\subset[0, 2\pi)$, of measure zero, a function $f(t)\in C(0, 2\pi)$, is constructed whose Fourier series is unboundedly divergent on $E$. If $E$ is closed, there is a function $\varphi(t)\in C(0,2\pi)$, whose Fourier series diverges unboundedly on $E$ and converges on $[0,2\pi)\setminus E$.

Full text: PDF file (703 kB)

English version:
Mathematical Notes, 1970, 7:1, 5–12

Bibliographic databases:

UDC: 517.5
Received: 05.05.1969

Citation: V. V. Buzdalin, “Unbounded divergence of Fourier series of continuous functions”, Mat. Zametki, 7:1 (1970), 7–18; Math. Notes, 7:1 (1970), 5–12

Citation in format AMSBIB
\Bibitem{Buz70}
\by V.~V.~Buzdalin
\paper Unbounded divergence of Fourier series of continuous functions
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 1
\pages 7--18
\mathnet{http://mi.mathnet.ru/mz6988}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=262757}
\zmath{https://zbmath.org/?q=an:0198.09402|0193.02902}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 1
\pages 5--12
\crossref{https://doi.org/10.1007/BF01093334}


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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. L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Russian Math. Surveys, 28:2 (1973), 65–127  mathnet  crossref  mathscinet  zmath
    2. V. V. Buzdalin, “Trigonometric Fourier series of continuous functions diverging on a given set”, Math. USSR-Sb., 24:1 (1974), 79–102  mathnet  crossref  mathscinet  zmath
    3. V. M. Bugadze, “On divergence of Fourier–Walsh series of bounded functions on sets of measure zero”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 365–372  mathnet  crossref  mathscinet  zmath  isi
    4. P. L. Ul'yanov, “Reminiscences of Sergei Borisovich Stechkin”, Russian Math. Surveys, 51:6 (1996), 1015–1024  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. G. A. Karagulyan, “Characterization of the sets of divergence for sequences of operators with the localization property”, Sb. Math., 202:1 (2011), 9–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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