Geodesic
Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs
Ural mathematical journal, Tome 3 (2017) no. 2, pp. 46-50 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, Сontinuous functions.
Mots-clés : Divergence at one point 
@article{UMJ_2017_3_2_a6,
     author = {Maxim L. Gridnev},
     title = {Divergence of the {Fourier} series of continuous functions with a restriction on the fractality of their graphs},
     journal = {Ural mathematical journal},
     pages = {46--50},
     year = {2017},
     volume = {3},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a6/}
}
TY  - JOUR
AU  - Maxim L. Gridnev
TI  - Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs
JO  - Ural mathematical journal
PY  - 2017
SP  - 46
EP  - 50
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a6/
LA  - en
ID  - UMJ_2017_3_2_a6
ER  - 
%0 Journal Article
%A Maxim L. Gridnev
%T Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs
%J Ural mathematical journal
%D 2017
%P 46-50
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a6/
%G en
%F UMJ_2017_3_2_a6
Maxim L. Gridnev. Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs. Ural mathematical journal, Tome 3 (2017) no. 2, pp. 46-50. http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a6/

[1] Bari N.K., Trigonometric series, Fizmatgiz, Moscow, 1961, 936 pp. (in Russian)

[2] Salem R., Essais sur les séries trigonométriques., v. 862, Actual. Sci. et Industr., 1940

[3] Waterman D., “On converges of Fourier series of functions of generalized bounded variation”, Studia Mathematica, 44 (1972), 107–117

[4] Gridnev M. L., “About classes of functions with a restriction on the fractality of their graphs”, Proceedings of the 48th Intern. Youth School-Conf.: Modern Problems in Mathematics and its Applications (Ekaterinburg, February 5–11, 2017), CEUR-WS Proceedings, 1894, 2017, 167–3 (in Russian) http://ceur-ws.org/Vol-1894/appr5.pdf