Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 47-63
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{FAA_2022_56_2_a4,
author = {D. L. Rogava},
title = {Approximation of {Operator} {Semigroups} {Using} {Linear-Fractional} {Operator} {Functions} and {Weighted} {Averages}},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {47--63},
publisher = {mathdoc},
volume = {56},
number = {2},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a4/}
}
TY - JOUR AU - D. L. Rogava TI - Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 2022 SP - 47 EP - 63 VL - 56 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a4/ LA - ru ID - FAA_2022_56_2_a4 ER -
D. L. Rogava. Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 47-63. http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a4/