AVERAGE KOLMOGOROV N-WIDTHS (N-K WIDTH) AND OPTIMAL INTERPOLATION OF SOBOLEV CLASS IN L_p(R)

The author obtains the exact values of the average n-K widths for some Sobolev classes defined by an ordinary differential operator P(D)=multiply from i=1 to r(D-t_il), t_i∈R, in the metric L_(R), 1≤p≤∞, and identifies some optimal subspaces. Furthermore, the optimal interpolation problem for these Sobolev classes is considered by sampling the function values at some countable sets of points distributed reasonably on R, and some exact results are obtained.