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

Abstract

We consider the generalized characteristics of smoothness of the functions $\omega^w(f, t)$ and $\Lambda^w(f, t), t > 0,$ in the space $L_2(R)$ and, on the classes $L^{\alpha}_2 (R)$ defined with the help of fractional-order derivatives $\alpha \in (0,\infty)$, obtain the exact Jackson-type inequalities for $\omega^w(f)$.