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Mat. Zametki, 1978, Volume 23, Issue 2, Pages 213–222 (Mi mz8134)  

This article is cited in 8 scientific papers (total in 8 papers)

A class of trigonometric series

G. A. Fomin

Kaluga State Pedagogical Institute

Abstract: Trigonometric series with coefficients $a_k\to0$ under the condition
$$ (\exists p\in R,p>1):(\sum_{n=1}^\infty\{\sum_{k=n}^\infty|\Delta a_k|^p/n\}^{1/p}<\infty). $$
are considered. It is shown that, under these conditions, the cosine series is a Fourier series for which the condition $a_n\ln n\to0$ is the criterion for convergence in the metric of $L$. For the sine series, this is true under the further assumption that $\sum_{n=1}^\infty|a_n|/n<\infty$.

Full text: PDF file (626 kB)

English version:
Mathematical Notes, 1978, 23:2, 117–123

Bibliographic databases:

UDC: 517.5
Received: 20.09.1976

Citation: G. A. Fomin, “A class of trigonometric series”, Mat. Zametki, 23:2 (1978), 213–222; Math. Notes, 23:2 (1978), 117–123

Citation in format AMSBIB
\Bibitem{Fom78}
\by G.~A.~Fomin
\paper A~class of trigonometric series
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 2
\pages 213--222
\mathnet{http://mi.mathnet.ru/mz8134}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=487218}
\zmath{https://zbmath.org/?q=an:0379.42004}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 2
\pages 117--123
\crossref{https://doi.org/10.1007/BF01153150}


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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. G. A. Fomin, “On convergence in the mean of Fourier series”, Math. USSR-Sb., 38:2 (1981), 231–244  mathnet  crossref  mathscinet  zmath  isi
    2. G. A. Fomin, “On some classes of Jacobi orthogonal series”, Math. USSR-Sb., 55:1 (1986), 121–132  mathnet  crossref  mathscinet  zmath
    3. O. I. Kuznetsova, “On a class of $N$-dimensional trigonometric series”, Math. Notes, 63:3 (1998), 352–356  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. K. Kaur, “Tauberian conditions for $L^1$-convergence of modified complex trigonometric sums”, Lobachevskii J. Math., 13 (2003), 39–44  mathnet  mathscinet  zmath
    5. A. S. Belov, “On Conditions of the Average Convergence (Upper Boundedness) of Trigonometric Series”, Journal of Mathematical Sciences, 155:1 (2008), 5–17  mathnet  crossref  mathscinet  zmath
    6. Kuznetsova O.I., “Strong Summability and Convergence of Multiple Trigonometric Series Over Polyhedrons”, J. Contemp. Math. Anal.-Armen. Aca., 47:5 (2012), 240–250  crossref  isi
    7. E. R. Liflyand, “Asymptotics of the Fourier Sine Transform of a Function of Bounded Variation”, Math. Notes, 100:1 (2016), 93–99  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Liflyand E., “The Fourier Transform of a Function of Bounded Variation: Symmetry and Asymmetry”, J. Fourier Anal. Appl., 24:2 (2018), 525–544  crossref  isi
  • Математические заметки Mathematical Notes
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