Geodesic
Approximation of functions of~$n$ variables by quasipolynomials
Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 568-586.

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Approximation of functions of $n$ variables is studied by means of infinite-dimensional subspaces of singular functions of a special form (quasipolynomials). In particular, best approximation is examined by means of these subspaces, and both direct and converse theorems are proved. 
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Yu. A. Brudnyi. Approximation of functions of~$n$ variables by quasipolynomials. Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 568-586. http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a6/

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