Geodesic
Estimates of the best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the multidimensional Jackson's theorem
Sbornik. Mathematics, Tome 188 (1997) no. 10, pp. 1507-1520 
N. N. Pustovoitov. Estimates of the best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the multidimensional Jackson's theorem. Sbornik. Mathematics, Tome 188 (1997) no. 10, pp. 1507-1520. http://geodesic.mathdoc.fr/item/SM_1997_188_10_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the first section the best approximations of periodic functions of one real variable by trigonometric polynomials are studied. Estimates of these approximations in terms of averaged differences are obtained. A multidimensional generalization of these estimates is presented in the second section. As a consequence. The multidimensional Jackson's theorem is proved.

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