KOLMOGOROV WIDTHS OF CLASSES OF PERIODIC-FUNCTIONS OF ONE AND SEVERAL VARIABLES

The order of Kolmogorov widths d(N)(W-approximately-pBAR-alphaBAR, L-approximately-q) are determined for the class W-approximately-pBAR-alphaBAR = intersection-1m W-approximately-p(i)-alpha-i that is the intersection of classes of periodic functions of one variable of "higher" smoothness, in the space L-approximately-q for 1 < q < infinity, and estimates from above for "low" smoothness, and also the order of Kolmogorov widths d(N)(H-approximately-p-r, L-approximately-q) is calculated for periodic functions of several variables in the space L-approximately-q for 1 < p less-than-or-equal-to q less-than-or-equal-to 2. The estimate from below for d(N) (H-approximately-p-r, L-approximately-q) reduces to the estimate from below of the width of a finite-dimensional set whose width is determined. Bibliography: 28 titles.