Geodesic
On the best convergence of multiple trigonometric series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 83-91

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

We consider the best convergence of multiple trigonometric series. We indicate essential distinction of the behavior (in this sense) of multiple series from that of simple ones. In particular, the well-known result obtained by S. N. Bernshtein on the best convergence of a series with an odd ratio of frequencies does not hold for a multiple series in the case of the approximation by polynomials with harmonics from rectangles (in the sense of Pringsheim), but it is true for “angular” approximations.
Keywords: the best convergence, summation over rectangles, summation “over angles”. 
@article{IVM_2008_5_a9,
     author = {A. I. Rubinshtein},
     title = {On the best convergence of multiple trigonometric series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--91},
     publisher = {mathdoc},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_5_a9/}
}
TY  - JOUR
AU  - A. I. Rubinshtein
TI  - On the best convergence of multiple trigonometric series
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 83
EP  - 91
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_5_a9/
LA  - ru
ID  - IVM_2008_5_a9
ER  - 
%0 Journal Article
%A A. I. Rubinshtein
%T On the best convergence of multiple trigonometric series
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 83-91
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2008_5_a9/
%G ru
%F IVM_2008_5_a9
A. I. Rubinshtein. On the best convergence of multiple trigonometric series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 83-91. http://geodesic.mathdoc.fr/item/IVM_2008_5_a9/