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Ural Mathematical Journal, 2017, Volume 3, Issue 2, Pages 46–50
DOI: https://doi.org/10.15826/umj.2017.2.007 (Mi umj42) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs

Maxim L. Gridnev

Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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DOI: https://doi.org/10.15826/umj.2017.2.007
Abstract: We consider certain classes of functions with a restriction on the fractality of their graphs. Modifying Lebesgue's example, we construct continuous functions from these classes whose Fourier series diverge at one point, i.e. the Fourier series of continuous functions from this classes do not converge everywhere.
Keywords: Trigonometric Fourier series, Fractality, Divergence at one point, Ñontinuous functions.
Funding agency Grant number
Russian Science Foundation 14-11-00702
This work was supported by the Russian Science Foundation (project no. 14-11-00702).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Maxim L. Gridnev, “Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs”, Ural Math. J., 3:2 (2017), 46–50
Citation in format AMSBIB
\Bibitem{Gri17}
\by Maxim~L.~Gridnev
\paper Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 2
\pages 46--50
\mathnet{http://mi.mathnet.ru/umj42}
\crossref{https://doi.org/10.15826/umj.2017.2.007}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR3746951}
\elib{https://elibrary.ru/item.asp?id=32334098}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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