Berdysheva, Elena E.; Filatova, Maria A. On the best approximation of the infinitesimal generator of a contraction semigroup in a Hilbert space. (English) Zbl 1448.41025 Ural Math. J. 3, No. 2, 40-45 (2017). Summary: 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 \(Q_2 = \{x\in \mathcal{D}(A^2) : \|A^2 x\| \leq 1\} \), where \(\mathcal D(A^2)\) denotes the domain of \(A^2\). Cited in 3 Documents MSC: 41A50 Best approximation, Chebyshev systems 47J25 Iterative procedures involving nonlinear operators Keywords:contraction semigroup; infinitesimal generator; Stechkin’s problem PDFBibTeX XMLCite \textit{E. E. Berdysheva} and \textit{M. A. Filatova}, Ural Math. J. 3, No. 2, 40--45 (2017; Zbl 1448.41025) Full Text: DOI MNR References: [1] Arestov V.V., “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093-1126 · Zbl 0947.41019 · doi:10.4213/rm1019 [2] Arestov V.V., Gabushin V.N., “Best approximation of unbounded operators by bounded operators”, Russian Math. (Iz. VUZ), 39:11 (1995), 38-63 · Zbl 0856.41018 [3] Arestov V.V., Filatova M.A., “Best approximation of the differentiation operator in the space \(L_2\) on the semiaxis”, J. Approx. Theory, 187 (2014), 65-81 · Zbl 1300.41015 · doi:10.1016/j.jat.2014.08.001 [4] Babenko V.F., Korneichuk N.P., Kofanov V.A., Pichugov S.A., Inequalities for derivatives and their applications, Naukova Dumka, Kiev, 2003 (in Russian) [5] Berdysheva E.E. On the best approximation of the differentiation operator in \(L_2(0,\infty)\), East J. Approx, 2:3 (1996), 281-287 · Zbl 0859.41021 [6] Grubb G., Distributions and Operators, Springer Science and Business Media, NY, 2008, 464 pp. · Zbl 1171.47001 · doi:10.1007/978-0-387-84895-2 [7] Hardy G.H., Littlewood J.E., Pólya G., Inequalities. Cambridge University Press, 1934. 314 p. · Zbl 0010.10703 [8] Hille E., Phillips R.S., Functional Analysis and Semigroups, American Mathematical Society, 1957, 808 pp. · Zbl 0078.10004 [9] Kato T., “On an inequality of Hardy, Littlewood and Pólya”, Adv. Math., 7 (1971), 217-218 · Zbl 0224.47021 · doi:10.1016/S0001-8708(71)80002-6 [10] Kato T., Perturbation Theory for Linear Operators, Springer, Verlag-Berlin-Heidelberg, 1995, 623 pp. · Zbl 0836.47009 · doi:10.1007/978-3-642-66282-9 [11] Stechkin S.B., “Best approximation of linear operators”, Math. Notes, 1 (1967), 91-99. · Zbl 0168.12201 · doi:10.1007/BF01268056 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.