Geodesic
On divergence of Fourier–Walsh series of continuous function
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2015), pp. 26-29.

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We prove that for any perfect set $P$ of positive measure, for which $0$ is a density point, one can construct a function $f(x)$ continuous on $[0,1)$ such that each measurable and bounded function, which coincides with $f(x)$ on the set $P$ has diverging Fourier–Walsh series at $0$.
Keywords: Fourier–Walsh series, continuous function
Mots-clés : divergence. 
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S. A. Sargsyan. On divergence of Fourier–Walsh series of continuous function. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2015), pp. 26-29. http://geodesic.mathdoc.fr/item/UZERU_2015_2_a4/

[1] D.E. Menshov, “On the Fourier Series of Continuous Functions”, Uch. Zapiski MGU. Matematika, 4 (1951), 108–132 (in Russian) | MR

[2] B.I Golubov, A.V. Efimov, V.A Skvortsov, Walsh Series and Transforms: Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1991 | MR | Zbl