Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space L2(ℝ). II

Abstract

In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness Λw on the classes of functions $$ {L}_2^{\alpha}\left(\iota \right) $$ defined by the fractional derivatives of order v 2 (0,1) in the space L2(ℝ). The exact values of the mean L2(ℝ) -widths for the classes of functions defined by the generalized characteristics of smoothness ew and Λw are also computed.