Extremal properties and two-sided estimates in approximation by sums of functions of lesser number of variables (Q1081041)

Let C be the space of the continuous functions defined on a closed interval in \({\mathbb{R}}^ n\) with the usual norm, and let N be a subspace of C, composed of sums of functions depending only on subsets of variables, chosen in a somewhat intricate manner. The author gives lower and upper estimates for the distance d(f,N), \(f\in C\). For a subspace W of C, he gives a formula for a ''projection'' on N. He considers also a subspace M of W, which is characterized by an equality between the distance and its lower estimate, true for each subinterval of the interval considered.