Vitalii V. Arestov     (Ural Federal University, Institute of Mathematics and Computer Science, Deparment of Mathematical Analysis and Function Theory, Ekaterinburg, Russian Federation)


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.


Differentiation operator; Stechkin's problem; Kolmogorov inequality

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DOI: http://dx.doi.org/10.15826/umj.2015.1.002

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