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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
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
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
Linking options:
https://www.mathnet.ru/eng/faa3942https://doi.org/10.4213/faa3942 https://www.mathnet.ru/eng/faa/v56/i2/p47
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Abstract page: | 228 | Full-text PDF : | 26 | References: | 57 | First page: | 23 |
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