Best approximation by ridge functions in L_p-spaces - Maiorov, V. E. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We study the approximation of the classes of functions by the manifold R_n formed by all possible linear combinations of n ridge functions of the form r(a · x)). It is proved that, for any 1 ≤ q ≤ p ≤ ∞, the deviation of the Sobolev class W^r_p from the set R_n of ridge functions in the space L_q (B^d) satisfies the sharp order n^-r/(d-1).