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Mat. Sb. (N.S.), 1979, Volume 110(152), Number 1(9), Pages 13–34 (Mi msb2421)  

This article is cited in 1 scientific paper (total in 1 paper)

On Fourier coefficients

P. L. Ul'yanov


Abstract: Let $\{\varphi_n\}$ be an orthonormal system of functions on the interval $[0,1]$, and let the function $f\in L^2(0, 1)$. We investigate the question of the convergence or divergence (depending on the smoothness of the function $f$) of series of the form
$$ \sum_{n = 1}^\infty|(f, \varphi_n)|^{\alpha_n}, $$
where $\alpha_n\uparrow2$ or $\alpha_n\to\alpha$ with $\alpha\in[0,2)$.
It is shown that in a certain sense, the assertions obtained are definitive for the Haar system.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1981, 38:1, 11–29

Bibliographic databases:

UDC: 517.5
MSC: Primary 42C15; Secondary 42C10
Received: 22.03.1979

Citation: P. L. Ul'yanov, “On Fourier coefficients”, Mat. Sb. (N.S.), 110(152):1(9) (1979), 13–34; Math. USSR-Sb., 38:1 (1981), 11–29

Citation in format AMSBIB
\Bibitem{Uly79}
\by P.~L.~Ul'yanov
\paper On Fourier coefficients
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 110(152)
\issue 1(9)
\pages 13--34
\mathnet{http://mi.mathnet.ru/msb2421}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=548514}
\zmath{https://zbmath.org/?q=an:0454.42004|0417.42024}
\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 1
\pages 11--29
\crossref{https://doi.org/10.1070/SM1981v038n01ABEH001047}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LB83400002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kudriavtsev D., “On the Fourier-Series of Functions Having a Fractional-Logarithmic Derivative”, 266, no. 2, 1982, 274–276  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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