Approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space L2(0,∞)

被引：0
|
作者：
V. V. Arestov
M. A. Filatova
机构：
[1] Ural Federal University,Institute of Mathematics and Computer Science
[2] Ural Branch of the Russian Academy of Sciences,Institute of Mathematics and Mechanics
来源：
Proceedings of the Steklov Institute of Mathematics | 2014年 / 284卷
关键词：
Stechkin’s problem; differentiation operator; semiaxis;
D O I：
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摘要：
We give an upper estimate for the value of the best approximation of the (firstorder) differentiation operator by linear bounded operators on the class of twice differentiable functions in the space L2(0,∞). This upper estimate is close to a known lower estimate and improves previously known upper estimates. To prove the upper estimate, we consider a specific family of operators; in this family, we choose an operator that provides the least estimate for the value of the best approximation.
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页码：24 / 40
页数：16
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