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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2009, Volume 6, Pages 17–25 (Mi semr54)  

Research papers

Divergence of the Fourier series of the Weierstrass–Mandelbrot cosine function

K. K. Kazbekov

Institute of Applied Mathematics and Informatics, Vladikavkaz Scientific Centre, RAS, Vladikavkaz, Russia
References:
Abstract: The set of $M_c$ – the points of divergence of the formal trigonometric Fourier series of the Weierstrass–Mandelbrot cosine function $C(t)$, given on the segment $[-1,1]$ is considered. In particular, it is shown that on the segment $[0,1]$ the Fourier series of the function $C(t)$ diverges in all the points of the subset $M_c(1/2)$, having zero measurement and the cardinality (power) of continuum when the function parameters are: $b=3$ and $D=1,5$.
Keywords: Fourier series, Weierstrass–Mandelbrot cosine function.
Received June 17, 2008, published February 6, 2009
Bibliographic databases:
Document Type: Article
UDC: 517.518.452
MSC: 42A16
Language: Russian
Citation: K. K. Kazbekov, “Divergence of the Fourier series of the Weierstrass–Mandelbrot cosine function”, Sib. Èlektron. Mat. Izv., 6 (2009), 17–25
Citation in format AMSBIB
\Bibitem{Kaz09}
\by K.~K.~Kazbekov
\paper Divergence of the Fourier series of the Weierstrass--Mandelbrot cosine function
\jour Sib. \`Elektron. Mat. Izv.
\yr 2009
\vol 6
\pages 17--25
\mathnet{http://mi.mathnet.ru/semr54}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2586677}
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