On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables

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.