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Mat. Zametki, 1968, Volume 3, Issue 4, Pages 449–460 (Mi mz6701)  

On Fourier coefficients of functions continued evenly or oddly

V. I. Prokhorenko


Abstract: Consideration is given to the question of how the orders of decrease of the Fourier coefficients of the two functions $F$ and $G$ are related, where $F$ and $G$ are, respectively, the odd and the even continuations onto the interval $[-\pi,0]$ of the function $f(x)\in L(0,\pi)$. It is shown that in passing from the one continuation to the other, an arbitrary rate of decrease of the Fourier coefficients is worsened, the degree of worsening depending on their initial rate of decrease.

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English version:
Mathematical Notes, 1968, 3:4, 286–293

Bibliographic databases:

UDC: 517.5
Received: 13.07.1967

Citation: V. I. Prokhorenko, “On Fourier coefficients of functions continued evenly or oddly”, Mat. Zametki, 3:4 (1968), 449–460; Math. Notes, 3:4 (1968), 286–293

Citation in format AMSBIB
\Bibitem{Pro68}
\by V.~I.~Prokhorenko
\paper On Fourier coefficients of functions continued evenly or oddly
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 4
\pages 449--460
\mathnet{http://mi.mathnet.ru/mz6701}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=226283}
\zmath{https://zbmath.org/?q=an:0169.39702}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 4
\pages 286--293
\crossref{https://doi.org/10.1007/BF01159947}


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  • http://mi.mathnet.ru/eng/mz/v3/i4/p449

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