Geodesic
On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables
Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 105-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a simple method for finding the values of the best approximation of a function of $n$ variables of a given class by means of sums of two functions of a fewer number of variables; we establish close upper and lower bounds for the value of the best approximation to the function $f(x_1,\dots,x_n)$, having the mixed derivative $f_{x_1\dots x_n}$, by means of sums of a function of $n-1$ variables. 
@article{MZM_1972_12_1_a13,
     author = {M. B. A. Babaev},
     title = {On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables},
     journal = {Matemati\v{c}eskie zametki},
     pages = {105--114},
     year = {1972},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a13/}
}
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M. B. A. Babaev. On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables. Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 105-114. http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a13/