Geodesic
Approximation of Classes of Periodic Functions in Several Variables
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 109-121 
A. S. Romanyuk. Approximation of Classes of Periodic Functions in Several Variables. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a9/
@article{MZM_2002_71_1_a9,
     author = {A. S. Romanyuk},
     title = {Approximation of {Classes} of {Periodic} {Functions} in {Several} {Variables}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {109--121},
     year = {2002},
     volume = {71},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a9/}
}
TY  - JOUR
AU  - A. S. Romanyuk
TI  - Approximation of Classes of Periodic Functions in Several Variables
JO  - Matematičeskie zametki
PY  - 2002
SP  - 109
EP  - 121
VL  - 71
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a9/
LA  - ru
ID  - MZM_2002_71_1_a9
ER  - 
%0 Journal Article
%A A. S. Romanyuk
%T Approximation of Classes of Periodic Functions in Several Variables
%J Matematičeskie zametki
%D 2002
%P 109-121
%V 71
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a9/
%G ru
%F MZM_2002_71_1_a9

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

We study the approximation of the classes $B_{p,\theta }^r$ and $W_{p,\alpha }^r$ of periodic functions of several variables by multiple Fourier sums of fixed order constructed with regard to individual properties of functions from these classes. In a number of cases, such approximations allow us to achieve a better degree of approximation of the classes indicated above as compared to their approximation by staircase hyperbolic Fourier sums.

[1] Temlyakov V. N., Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi, Tr. MIAN, 178, Nauka, M., 1986 | MR | Zbl

[2] Kashin B. S., Temlyakov V. N., “O nailuchshikh $m$-chlennykh priblizheniyakh i entropii mnozhestv v prostranstve $L_1$”, Matem. zametki, 56:5 (1994), 57–86 | MR | Zbl

[3] Lizorkin P. I., Nikolskii S. M., “Prostranstva funktsii smeshannoi gladkosti s dekompozitsionnoi tochki zreniya”, Tr. MIAN, 187, Nauka, M., 1989, 143–161 | MR

[4] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969

[5] Belinskii E. S., “Priblizhenie plavayuschei sistemoi eksponent na klassakh periodicheskikh funktsii s ogranichennoi smeshannoi proizvodnoi”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, YaGU, Yaroslavl, 1988, 16–33 | MR

[6] Romanyuk A. S., “Priblizhenie klassov Besova periodicheskikh funktsii mnogikh peremennykh v prostranstve $L_q$”, Ukr. matem. zh., 43:10 (1991), 1398–1408 | MR | Zbl

[7] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987

[8] Galeev E. M., “Poryadkovye otsenki proizvodnykh periodicheskogo mnogomernogo $\alpha$-yadra Dirikhle v smeshannoi norme”, Matem. sb., 117:1 (1982), 32–43 | MR | Zbl

[9] Galeev E. M., “Priblizhenie klassov periodicheskikh funktsii neskolkikh peremennykh yadernymi operatorami”, Matem. zametki, 47:3 (1990), 32–41 | MR | Zbl

[10] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | Zbl