### 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

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