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Funktsional'nyi Analiz i ego Prilozheniya, 2022, Volume 56, Issue 2, Pages 47–63
DOI: https://doi.org/10.4213/faa3942
(Mi faa3942)
 

Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages

D. L. Rogava

Tbilisi Ivane Javakhishvili State University, Ilia Vekua Institute of Applied Mathematics
References:
Abstract: An analytic semigroup of operators on a Banach space is approximated by a sequence of positive integer powers of a linear-fractional operator function. It is proved that the order of the approximation error in the domain of the generating operator equals $O(n^{-2}\ln(n))$. For a self-adjoint positive definite operator $A$ decomposed into a sum of self-adjoint positive definite operators, an approximation of the semigroup {$\exp(-tA)$} ($t\geq0$) by weighted averages is also considered. It is proved that the order of the approximation error in the operator norm equals $O(n^{-1/2}\ln(n))$.
Keywords: approximation of semigroup, Trotter–Chernoff formula, analytic semigroup.
Received: 07.09.2021
Revised: 06.12.2021
Accepted: 07.12.2021
English version:
Functional Analysis and Its Applications, 2022, Volume 56, Issue 2, Pages 116–129
DOI: https://doi.org/10.1134/S0016266322020058
Bibliographic databases:
Document Type: Article
UDC: 517.983.23, 517.983.246
Language: Russian
Citation: D. L. Rogava, “Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages”, Funktsional. Anal. i Prilozhen., 56:2 (2022), 47–63; Funct. Anal. Appl., 56:2 (2022), 116–129
Citation in format AMSBIB
\Bibitem{Rog22}
\by D.~L.~Rogava
\paper Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages
\jour Funktsional. Anal. i Prilozhen.
\yr 2022
\vol 56
\issue 2
\pages 47--63
\mathnet{http://mi.mathnet.ru/faa3942}
\crossref{https://doi.org/10.4213/faa3942}
\transl
\jour Funct. Anal. Appl.
\yr 2022
\vol 56
\issue 2
\pages 116--129
\crossref{https://doi.org/10.1134/S0016266322020058}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85139683894}
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    Функциональный анализ и его приложения Functional Analysis and Its Applications
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