DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS

Maxim L. Gridnev     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russian Federation)

Abstract


We consider certain classes of functions with a restriction on the fractality of their graphs. Modifying Lebesgue’s example, we construct continuous functions from these classes whose Fourier series diverge at one point, i.e. the Fourier series of continuous functions from this classes do not converge everywhere.


Keywords


Trigonometric Fourier series, Fractality, Divergence at one point, Сontinuous functions

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References


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  4. Gridnev M. L. About classes of functions with a restriction on the fractality of their graphs // CEUR-WS Proceedings, 2017. Vol.1894: Proceedings of the 48th Intern. Youth School-Conf.: Modern Problems in Mathematics and its Applications, Ekaterinburg, February 5–11, 2017. P. 167–173. http://ceur-ws.org/Vol-1894/appr5.pdf [in Russian].



DOI: http://dx.doi.org/10.15826/umj.2017.2.007

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