Geodesic
Approximation of functions of several variables, taking account of the growth of the coefficients of the approximating combinations
Sbornik. Mathematics, Tome 39 (1981) no. 1, pp. 133-143 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that every continuous function defined on the $n$-dimensional rectangular parallelepiped $\{x=(x_1,\dots,x_n)\in\mathbf R^n:0\leqslant x_i\leqslant a_i,\ 1\leqslant i\leqslant n\}$ can be approximated by polynomials of the form $Q(x)=\sum^p_{|\alpha|=0}c_\alpha x^\alpha$, where $c_\alpha=\eta_\alpha M(\alpha)$, with $\sum^p_{|\alpha|=0}|\eta_\alpha|\leqslant1$. Here $M(\alpha)$ is an arbitrary positive function defined on the set of multi-indices, and $\lim_{|\alpha|\to\infty}\sqrt[|\alpha|]{M(\alpha)}=\infty$. Bibliography: 9 titles. 
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V. V. Napalkov. Approximation of functions of several variables, taking account of the growth of the coefficients of the approximating combinations. Sbornik. Mathematics, Tome 39 (1981) no. 1, pp. 133-143. http://geodesic.mathdoc.fr/item/SM_1981_39_1_a6/

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