Jackson-Type Inequalities for the Special Moduli of Continuity on the Entire Real Axis and the Exact Values of Mean nu - Widths for the Classes of Functions in the Space L (2) (R)

摘要

The exact values of constants are obtained in the space L (2)(a"e) for the Jackson-type inequalities for special moduli of continuity of the k th order defined by the Steklov operator S (h) () instead of the translation operator T (h) () in the case of approximation by entire functions of exponential type sigma a (0,a) . The exact values of the mean nu -widths (linear, Bernstein, and Kolmogorov) are also obtained for the classes of functions defined by the indicated characteristic of smoothness.