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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2009, Volume 6, Pages 17–25
(Mi semr54)
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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.
Received June 17, 2008, published February 6, 2009
Citation:
K. K. Kazbekov, “Divergence of the Fourier series of the Weierstrass–Mandelbrot cosine function”, Sib. Èlektron. Mat. Izv., 6 (2009), 17–25
Linking options:
https://www.mathnet.ru/eng/semr54 https://www.mathnet.ru/eng/semr/v6/p17
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Abstract page: | 568 | Full-text PDF : | 175 | References: | 62 |
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