Stechkin's Problem on the Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line

Stechkin's problem of the best approximation of differentiation operators by bounded linear operators on the half-line in the uniform norm is studied. The structure of the best approximation operator is investigated, and its relationship to the spline dual (in the sense of N. P. Kuptsov) to the extremal spline in the Landau–Kolmogorov inequality on the half-line is examined.