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. 
@article{IM2_1970_4_3_a6,
     author = {Yu. A. Brudnyi},
     title = {Approximation of functions of~$n$ variables by quasipolynomials},
     journal = {Izvestiya. Mathematics },
     pages = {568--586},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a6/}
}
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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/