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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 2(6), Pages 224–237 (Mi msb3206)  

This article is cited in 2 scientific papers (total in 2 papers)

Everywhere divergent trigonometric series

A. S. Belov


Abstract: This paper establishes the existence of everywhere divergent trigonometric series with various kinds of gaps.
It is shown, for example, that for every positive integer $\lambda$ there are $r_n\to0$ and $\gamma_n$ such that $\sum_{n=1}^\infty r_n\cos(n^\lambda x-\gamma_n+\varphi)$ diverges tor all $x$ and $\varphi$ in $(-\infty,+\infty)$.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:2, 219–232

Bibliographic databases:

UDC: 517.522.3
MSC: 42A20
Received: 10.06.1970

Citation: A. S. Belov, “Everywhere divergent trigonometric series”, Mat. Sb. (N.S.), 85(127):2(6) (1971), 224–237; Math. USSR-Sb., 14:2 (1971), 219–232

Citation in format AMSBIB
\Bibitem{Bel71}
\by A.~S.~Belov
\paper Everywhere divergent trigonometric series
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 2(6)
\pages 224--237
\mathnet{http://mi.mathnet.ru/msb3206}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=301436}
\zmath{https://zbmath.org/?q=an:0216.39202}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 2
\pages 219--232
\crossref{https://doi.org/10.1070/SM1971v014n02ABEH002614}


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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. P. L. Ul'yanov, “Luzin's work on the metric theory of functions”, Russian Math. Surveys, 40:3 (1985), 15–77  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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