Best approximation of the differentiation operator in the space \(L_2\) on the semiaxis

DOI10.1016/j.jat.2014.08.001zbMath1300.41015OpenAlexW1980121273MaRDI QIDQ744065

M. A. Filatova, Vitalii Arestov

Publication date: 6 October 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2014.08.001

zbMATH Keywords

best approximationoptimal recoverydifferentiation operatorStechkin's problem

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Approximation by operators (in particular, by integral operators) (41A35) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Approximation by other special function classes (41A30)

Related Items (7)

Best uniform approximation of the differentiation operator by operators bounded in the space \(L_2\) ⋮ Three extremal problems in the Hardy and Bergman spaces of functions analytic in a disk ⋮ ON THE BEST APPROXIMATION OF THE INFINITESIMAL GENERATOR OF A CONTRACTION SEMIGROUP IN A HILBERT SPACE ⋮ Uniform approximation of differentiation operators by bounded linear operators in the space \(L_r\) ⋮ Optimal recovery of a derivative of an analytic function from values of the function given with an error on a part of the boundary ⋮ An analogue of the two-constants theorem and optimal recovery of analytic functions ⋮ Analog of the Hadamard theorem and related extremal problems on the class of analytic functions

Cites Work

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• Approximation of differentiation operator in the space \(L_2\) on semiaxis
• Approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space \(L_2(0,\infty)\)
• Uniform regularization of the problem of calculating the values of an operator
• Kolmogorov estimates for derivatives in \(L_2[0,\infty)\)
• Approximation of operators invariant with respect to a shift
• Norm inequalities for derivatives and differences
• Best approximation of unbounded operators by bounded ones
• Stechkin's problem for differential operators and functionals of first and second orders
• Inequalities for the norms of a function and its derivatives in metric \(L_ p\)
• Best approximation of linear operators
• On an inequality of Hardy, Littlewood, and Pólya
• Best approximations in \(L_{[0,\infty)}\) of the differentiation operator
• The best approximation of the differentiation operator in the metric of L\(_p\)
• On a Class of Integral Inequalities
• Approximation of unbounded operators by bounded operators and related extremal problems

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