Abstract:
Let A be the infinitesimal generator of a strongly continuous contraction semigroup in a Hilbert space H. We give an upper estimate for the best approximation of the operator A by bounded linear operators with a prescribed norm in the space H on the class Q2={x∈D(A2):‖A2x‖≤1}, where D(A2) denotes the domain of A2.
This work was supported by the Russian Foundation for Basic Research (project no. 15-01-02705), the Program for State Support of Leading Scientific Schools of the Russian Federation (project no. NSh-9356.2016.1), and by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and the Ural Federal University.
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Document Type:
Article
Language: English
Citation:
Elena E. Berdysheva, Maria A. Filatova, “On the best approximation of the infinitesimal generator of a contraction semigroup in a Hilbert space”, Ural Math. J., 3:2 (2017), 40–45
\Bibitem{BerFil17}
\by Elena~E.~Berdysheva, Maria~A.~Filatova
\paper On the best approximation of the infinitesimal generator of a contraction semigroup in a Hilbert space
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 2
\pages 40--45
\mathnet{http://mi.mathnet.ru/umj41}
\crossref{https://doi.org/10.15826/umj.2017.2.006}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR3746950}
\elib{https://elibrary.ru/item.asp?id=32334097}
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This publication is cited in the following 3 articles:
Platon G. Surkov, “Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach”, Fract Calc Appl Anal, 24:3 (2021), 895
V. Arestov, “Uniform Approximation of Differentiation Operators by Bounded Linear Operators in the Space Lr”, Anal Math, 46:3 (2020), 425
V. V. Arestov, “Best Uniform Approximation of the Differentiation Operator by Operators Bounded in the Space L2”, Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S9–S30
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