Geodesic
Sequences of rectangular Fourier sums of continuous functions with given majorants of the mixed moduli of smoothness
Sbornik. Mathematics, Tome 187 (1996) no. 7, pp. 981-1004 
O. V. Davydov. Sequences of rectangular Fourier sums of continuous functions with given majorants of the mixed moduli of smoothness. Sbornik. Mathematics, Tome 187 (1996) no. 7, pp. 981-1004. http://geodesic.mathdoc.fr/item/SM_1996_187_7_a1/
@article{SM_1996_187_7_a1,
     author = {O. V. Davydov},
     title = {Sequences of rectangular {Fourier} sums of continuous functions with given majorants of the~mixed moduli of smoothness},
     journal = {Sbornik. Mathematics},
     pages = {981--1004},
     year = {1996},
     volume = {187},
     number = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_7_a1/}
}
TY  - JOUR
AU  - O. V. Davydov
TI  - Sequences of rectangular Fourier sums of continuous functions with given majorants of the mixed moduli of smoothness
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 981
EP  - 1004
VL  - 187
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_7_a1/
LA  - en
ID  - SM_1996_187_7_a1
ER  - 
%0 Journal Article
%A O. V. Davydov
%T Sequences of rectangular Fourier sums of continuous functions with given majorants of the mixed moduli of smoothness
%J Sbornik. Mathematics
%D 1996
%P 981-1004
%V 187
%N 7
%U http://geodesic.mathdoc.fr/item/SM_1996_187_7_a1/
%G en
%F SM_1996_187_7_a1

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

Approximation by the rectangular Fourier sums $S_N(f)$ is studied for classes of functions of several variables defined in terms of the orders of decrease of the mixed moduli of smoothness. The problem of the existence of a single (independent of $N$) function $f$ on which the order of the approximation in the corresponding class is realized is solved.

[1] Menchoff D. E., “Sur les sommes partielles des séries de Fourier des fonctions continues”, Matem. sb., 15 (57):3 (1944), 385–432 | MR | Zbl

[2] Oskolkov K. I., “Podposledovatelnosti summ Fure funktsii s zadannym modulem nepreryvnosti”, Matem. sb., 88 (130):3(7) (1972), 447–469 | MR | Zbl

[3] Zigmund A., Trigonometricheskie ryady, T. 1, Mir, M., 1965 | MR

[4] Davydov O. V., “O priblizhenii individualnykh funktsii pryamougolnymi summami Fure”, DAN, 327:3 (1992), 295–298 | MR | Zbl

[5] Potapov M. K., “Izuchenie nekotorykh klassov funktsii pri pomoschi priblizheniya “uglom””, Tr. MIAN, 117, Nauka, M., 1972, 256–291 | MR | Zbl

[6] Zhizhiashvili L. V., Sopryazhennye funktsii i trigonometricheskie ryady, Izd-vo Tbil. un-ta, Tbilisi, 1969 | MR

[7] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960

[8] Pavliashvili G. G., “O priblizhenii funktsii mnogikh peremennykh summami Fure”, Soobscheniya AN GSSR, chast II, 134:3 (1989), 29–32 | MR

[9] Gelfond A. O., Ischislenie konechnykh raznostei, Nauka, M., 1967 | MR