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Mat. Sb. (N.S.), 1974, Volume 93(135), Number 2, Pages 203–217 (Mi msb2971)  

This article is cited in 10 scientific papers (total in 10 papers)

On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions

S. V. Bochkarev


Abstract: The paper is devoted to the absolute convergence of Fourier series of absolutely continuous functions in arbitrary bounded complete orthonormal systems of functions. The results obtained are new even for the classical systems, namely the trigonometric system and the Walsh system.
Bibliography: 8 titles.

Full text: PDF file (1103 kB)
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English version:
Mathematics of the USSR-Sbornik, 1974, 22:1, 201–216

Bibliographic databases:

UDC: 517.522.3
MSC: 42A28, 42A60
Received: 26.04.1973

Citation: S. V. Bochkarev, “On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions”, Mat. Sb. (N.S.), 93(135):2 (1974), 203–217; Math. USSR-Sb., 22:1 (1974), 201–216

Citation in format AMSBIB
\Bibitem{Boc74}
\by S.~V.~Bochkarev
\paper On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 93(135)
\issue 2
\pages 203--217
\mathnet{http://mi.mathnet.ru/msb2971}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=346410}
\zmath{https://zbmath.org/?q=an:0285.42015}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 22
\issue 1
\pages 201--216
\crossref{https://doi.org/10.1070/SM1974v022n02ABEH001691}


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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. S. V. Bochkarev, “A Fourier series in an arbitrary bounded orthonormal system that diverges on a set of positive measure”, Math. USSR-Sb., 27:3 (1975), 393–405  mathnet  crossref  mathscinet  zmath
    2. B. S. Kashin, “Remarks on estimating the Lebesgue functions of an orthonormal system”, Math. USSR-Sb., 35:1 (1979), 57–62  mathnet  crossref  mathscinet  zmath  isi
    3. S. V. Bochkarev, “Multiplicative Inequalities for Functions from the Hardy Space $H^1$ and Their Application to the Estimation of Exponential Sums”, Proc. Steklov Inst. Math., 243 (2003), 89–97  mathnet  mathscinet  zmath
    4. Bochkarev S., “New Multiplicative Inequalities and Estimates for the l-1-Norms of Trigonometric Series and Polynomials”, Dokl. Math., 72:2 (2005), 762–765  mathnet  mathscinet  zmath  isi
    5. S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64  mathnet  crossref  mathscinet  elib
    6. S. V. Bochkarev, “Multiplicative Bounds for $L_1$-Norms of Exponential Sums”, Journal of Mathematical Sciences, 155:1 (2009), 47–56  mathnet  crossref  mathscinet
    7. S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. S. V. Bochkarev, “de la Vallée-Poussin means of Fourier series for the quadratic spectrum and for spectra with power-like density”, Russian Math. Surveys, 69:1 (2014), 119–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Sb. Math., 209:11 (2018), 1575–1602  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. V. Sh. Tsagareishvili, G. Tutberidze, “Multipliers of Absolute Convergence”, Math. Notes, 105:3 (2019), 439–448  mathnet  crossref  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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