WIDTHS IN $ L_p$ OF CLASSES OF CONTINUOUS AND OF DIFFERENTIABLE FUNCTIONS, AND OPTIMAL METHODS OF CODING AND RECOVERING FUNCTIONS AND THEIR DERIVATIVES

Abstract

Exact values of linear widths (diameters), Kolmogorov widths and Gel'fand widths, in -spaces are found for some classes of functions, using a convex majorant of the modulus of continuity of a function or its derivative. Precise constants in the Jackson type theorems on approximation of continuous and differentiable functions are also found. These results are interpreted from the point of view of problems of optimal coding and optimal recovery of functions and their derivatives. Bibliography: 23 titles.