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...
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| Language: | English |
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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
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/103 |
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| author | Maxim L. Gridnev |
| author_facet | Maxim L. Gridnev |
| author_sort | Maxim L. Gridnev |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7912a1d6cfb7479eb044bd77f87c1a03 |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2017-12-01 |
| publisher | 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 |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-7912a1d6cfb7479eb044bd77f87c1a032025-08-20T02:52:21ZengUral 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 MechanicsUral Mathematical Journal2414-39522017-12-013210.15826/umj.2017.2.00746DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHSMaxim L. Gridnev0Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, EkaterinburgWe 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.https://umjuran.ru/index.php/umj/article/view/103Trigonometric Fourier series, Fractality, Divergence at one point, Сontinuous functions |
| spellingShingle | Maxim L. Gridnev DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS Ural Mathematical Journal Trigonometric Fourier series, Fractality, Divergence at one point, Сontinuous functions |
| title | DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS |
| title_full | DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS |
| title_fullStr | DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS |
| title_full_unstemmed | DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS |
| title_short | DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS |
| title_sort | divergence of the fourier series of continuous functions with a restriction on the fractality of their graphs |
| topic | Trigonometric Fourier series, Fractality, Divergence at one point, Сontinuous functions |
| url | https://umjuran.ru/index.php/umj/article/view/103 |
| work_keys_str_mv | AT maximlgridnev divergenceofthefourierseriesofcontinuousfunctionswitharestrictiononthefractalityoftheirgraphs |