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

D. L. Rogava

Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 47-63

Résumé

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 $O(n^{-1/2}\ln(n))$.

Détail

Keywords: approximation of semigroup, Trotter–Chernoff formula, analytic semigroup.