Geodesic
On Bohr's theorem for multiple Fourier series
Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 913-924 
A. A. Sahakian. On Bohr's theorem for multiple Fourier series. Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 913-924. http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a11/
@article{MZM_1998_64_6_a11,
     author = {A. A. Sahakian},
     title = {On {Bohr's} theorem for multiple {Fourier} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {913--924},
     year = {1998},
     volume = {64},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a11/}
}
TY  - JOUR
AU  - A. A. Sahakian
TI  - On Bohr's theorem for multiple Fourier series
JO  - Matematičeskie zametki
PY  - 1998
SP  - 913
EP  - 924
VL  - 64
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a11/
LA  - ru
ID  - MZM_1998_64_6_a11
ER  - 
%0 Journal Article
%A A. A. Sahakian
%T On Bohr's theorem for multiple Fourier series
%J Matematičeskie zametki
%D 1998
%P 913-924
%V 64
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a11/
%G ru
%F MZM_1998_64_6_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of Pringsheim uniform convergence of multiple Fourier series in the trigonometric system is considered. A multidimensional analog of Bohr's theorem on the uniform convergence of the Fourier series of a continuous function after a homeomorphic chance of variable is proved.

[1] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961

[2] Kahane J.-P., Katznelson Y., “Series de Fourier des functions bornées”, A la Memoire de P. Turan, Stud. Pure Math., Akad. Kiadó, Budapest, 1983, 395–410 | MR

[3] Saakyan A. A., “O svoistvakh koeffitsientov Fure superpozitsii funktsii”, Dokl. AN SSSR, 248:2 (1979), 302–306 | MR | Zbl

[4] Saakyan A. A., “O teoreme Bora dlya kratnykh trigonometricheskikh ryadov”, Matem. zametki, 46:2 (1989), 94–103 | MR | Zbl

[5] Golubov B. I., “Dvoinye ryady Fure i funktsii ogranichennoi variatsii”, Izv. vuzov. Matem., 1972, no. 12 (127), 55–68 | MR | Zbl

[6] Saakyan A. A., “O skhodimosti dvoinykh ryadov Fure funktsii ogranichennoi garmonicheskoi variatsii”, Izv. AN ArmSSR. Matem., 21:6 (1986), 517–529 | MR

[7] Waterman D., “On convergence of Fourier series of functions of generalized bounded variation”, Studia Math., 44:1 (1976), 107–117