On the best approximation of the differentiation operator on the half-line

We solve a problem of S. B. Stechkin concerning the best approximation in the metric of $C$ to the operator of $k$-th order differentiation on certain classes of differentiable functions defined on the half-line, by linear operators whose norms from $L_2$ into $C$ are bounded. We consider the analogous problem for linear differential operators with constant coefficients.