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

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

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 conver...

Full description

Saved in:
Bibliographic Details
Main Author: Maxim L. Gridnev
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2017-12-01
Series:Ural Mathematical Journal
Subjects:
Trigonometric Fourier series, Fractality, Divergence at one point, Сontinuous functions
Online Access:https://umjuran.ru/index.php/umj/article/view/103
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2414-3952

Similar Items