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Mat. Zametki, 1974, Volume 15, Issue 4, Pages 527–532 (Mi mz7375)  

Fourier sums for the Banach indicatrix

K. I. Oskolkov

Steklov Mathematical Institute, Academy of Sciences of the USSR

Abstract: We prove the existence of a function $f(t)$, which is continuous on the interval $[0,1]$, is of bounded variation, $\min f(t)=0$, $\max f(t)=1$, for which the integral
$$ I(x)=\frac1\pi\int_0^\infty[\int_0^1\cos y(f(t)-x)|df(t)|] dy $$
diverges for almost all $x\in[0,1]$. This result gives a negative answer to a question posed by Z. Ciesielski.

Full text: PDF file (398 kB)

English version:
Mathematical Notes, 1974, 15:4, 309–312

Bibliographic databases:

UDC: 517.5
Received: 02.11.1973

Citation: K. I. Oskolkov, “Fourier sums for the Banach indicatrix”, Mat. Zametki, 15:4 (1974), 527–532; Math. Notes, 15:4 (1974), 309–312

Citation in format AMSBIB
\Bibitem{Osk74}
\by K.~I.~Oskolkov
\paper Fourier sums for the Banach indicatrix
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 4
\pages 527--532
\mathnet{http://mi.mathnet.ru/mz7375}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=357709}
\zmath{https://zbmath.org/?q=an:0322.42015|0315.42013}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 4
\pages 309--312
\crossref{https://doi.org/10.1007/BF01095119}


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