ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR

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

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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References


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

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