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

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