Geodesic
Fourier Coefficients of Functions with a Given Modulus of Continuity
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 184-192 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we study the role of the convexity condition for the modulus of continuity in the problem of finding an upper bound for the Fourier coefficients taken over the class of functions with a given modulus of continuity. Also, we solve the problem of the Fourier coefficients for the Rademacher system.
Mots-clés : Fourier coefficient
Keywords: modulus of continuity of a function, system of Rademacher functions, $2\pi$-periodic function, convex function. 
@article{MZM_2007_81_2_a2,
     author = {V. S. Biryukova},
     title = {Fourier {Coefficients} of {Functions} with a {Given} {Modulus} of {Continuity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {184--192},
     year = {2007},
     volume = {81},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a2/}
}
TY  - JOUR
AU  - V. S. Biryukova
TI  - Fourier Coefficients of Functions with a Given Modulus of Continuity
JO  - Matematičeskie zametki
PY  - 2007
SP  - 184
EP  - 192
VL  - 81
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a2/
LA  - ru
ID  - MZM_2007_81_2_a2
ER  - 
%0 Journal Article
%A V. S. Biryukova
%T Fourier Coefficients of Functions with a Given Modulus of Continuity
%J Matematičeskie zametki
%D 2007
%P 184-192
%V 81
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a2/
%G ru
%F MZM_2007_81_2_a2
V. S. Biryukova. Fourier Coefficients of Functions with a Given Modulus of Continuity. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 184-192. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a2/

[1] H. Lebesgue, “Sur la représentation trigonométrique approcheé des fonctions satisfaisant á une condition de Lipschitz”, Bull. Soc. Math. France, 38 (1910), 184–210 | MR | Zbl

[2] S. M. Nikolskii, “Ryad Fure funktsii s dannym modulem nepreryvnosti”, Dokl. AN SSSR, 52:3 (1946), 101–104 | MR | Zbl

[3] A. V. Efimov, “Priblizhenie nepreryvnykh periodicheskikh funktsii summami Fure”, Izv. AN SSSR. Ser. matem., 24 (1960), 243–296 | MR | Zbl

[4] S. M. Nikolskii, “Nekotorye voprosy priblizhenii funktsii polinomami”, Mezhdunarodnyi matematicheskii kongress v Amsterdame, Obzornye doklady (1954), GIFML, M., 1961, 259–281 | MR | Zbl

[5] N. Burbaki, Funktsii deistvitelnogo peremennogo, Nauka, M., 1965 | MR | Zbl

[6] I. P. Natanson, Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974 | MR | Zbl

[7] A. V. Efimov, “O verkhnikh granyakh koeffitsientov Fure–Uolsha”, Matem. zametki, 6:6 (1969), 725–736 | MR | Zbl