О ПРИБЛИЖЕНИИ ОПЕРАТОРА ДИФФЕРЕНЦИРОВАНИЯ ЛИНЕЙНЫМИ ОГРАНИЧЕННЫМИ ОПЕРАТОРАМИ НА КЛАССЕ ДВАЖДЫ ДИФФЕРЕНЦИРУЕМЫХ ФУНКЦИЙ В ПРОСТРАНСТВЕ L2 (0,∞).

Translated title of the contribution: On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space L2 (0,∞)

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Abstract

We give an upper bound for the error of the best approximation of the (first-order) differentiation operator by linear bounded operators on the class of twice differentiable functions in the space L2 (0,∞). This upper bound is close to a known lower bound and improves the previous upper bounds. To prove the upper estimate, we consider a specific family of operators; in this family, we choose an operator that provides the least bound for the error of the best approximation.
Translated title of the contributionOn the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space L2 (0,∞)
Original languageRussian
Pages (from-to)35-50
Number of pages6
JournalТруды института математики и механики УрО РАН
Volume18
Issue number4
Publication statusPublished - 2012

GRNTI

  • 27.00.00 MATHEMATICS

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  • VAK List

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