ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR

Abstract

In this paper we give a solution of the problem of the best approximation in the uniform norm of the differentiation operator of order k by bounded linear operators in the class of functions with the property that the Fourier transforms of their derivatives of order n (0 < k <n) are finite measures. We also determine the exact value of the best constant in the corresponding inequality for derivatives.

Keywords

• Differentiation operator
• Stechkin's problem
• Kolmogorov inequality