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Mat. Zametki, 1977, Volume 22, Issue 1, Pages 77–83 (Mi mz8027)  

Trigonometric series with monotone coefficients

L. A. Balashov

M. V. Lomonosov Moscow State University

Abstract: Let $\{a_n\}$ be a monotonically decreasing sequence. Then each sequence $\{b_n\}$ such that $b_n\downarrow0$, $b_n\le a_n$, $n=1,2,…$, is a sequence of Fourier-Lebesgue coefficients with respect to the system $\{\cos nx\}$ if and only if the sequence $\sum_{n=1}^\infty\frac{a_n}n$ converges.

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English version:
Mathematical Notes, 1977, 22:1, 533–536

Bibliographic databases:

UDC: 517.5
Received: 04.06.1974

Citation: L. A. Balashov, “Trigonometric series with monotone coefficients”, Mat. Zametki, 22:1 (1977), 77–83; Math. Notes, 22:1 (1977), 533–536

Citation in format AMSBIB
\Bibitem{Bal77}
\by L.~A.~Balashov
\paper Trigonometric series with monotone coefficients
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 1
\pages 77--83
\mathnet{http://mi.mathnet.ru/mz8027}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=447952}
\zmath{https://zbmath.org/?q=an:0356.42002}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 1
\pages 533--536
\crossref{https://doi.org/10.1007/BF01147695}


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