Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space $L_2 (R)$. II

Abstract

In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness $\Lambda^w$ on the classes of functions $L^{\alpha}_2 (R)$ defined by the fractional derivatives of order $\alpha \in (0,\infty )$ in the space $L_2(R)$. The exact values of the mean $\nu$ -widths for the classes of functions, defined by the generalized characteristics of smoothness $\omega w$ and $\Lambda w$ are also computed in $L_2(R)$.