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 Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 5, Pages 3–12 (Mi ivm8793)

Approximation of differentiation operator in the space $L_2$ on semiaxis

V. V. Arestovab, M. A. Filatovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
b Chair of Mathematical Analysis and Function Theory, Ural Federal University, Yekaterinburg, Russia

Abstract: We establish an upper bound for the error of the best approximation of the first order differentiation operator by linear bounded operators on the set of twice differentiable functions in the space $L_2$ on the half-line. This upper bound is close to a known lower bound and improves the previously known upper bound due to E. E. Berdysheva. We use a specific operator that is introduced and studied in the paper.

Keywords: Stechkin problem, optimal recovery, differential operator, half-line.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:5, 1–8
UDC: 517.518+517.983

Citation: V. V. Arestov, M. A. Filatova, “Approximation of differentiation operator in the space $L_2$ on semiaxis”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 5, 3–12; Russian Math. (Iz. VUZ), 57:5 (2013), 1–8

Citation in format AMSBIB
\Bibitem{AreFil13} \by V.~V.~Arestov, M.~A.~Filatova \paper Approximation of differentiation operator in the space $L_2$ on semiaxis \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2013 \issue 5 \pages 3--12 \mathnet{http://mi.mathnet.ru/ivm8793} \transl \jour Russian Math. (Iz. VUZ) \yr 2013 \vol 57 \issue 5 \pages 1--8 

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This publication is cited in the following articles:
1. Arestov V., Filatova M., “Best Approximation of the Differentiation Operator in the Space l-2 on the Semiaxis”, J. Approx. Theory, 187 (2014), 65–81
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