Geodesic
On the best convergence of multiple trigonometric series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 83-91 Cet article a éte moissonné depuis la source Math-Net.Ru

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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”. 
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     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},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_5_a9/}
}
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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/

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