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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 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

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.

UDC: 517.518.452

MSC: 42A16

Received June 17, 2008, published February 6, 2009



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