Rational approximation of operator semigroups via the $\mathcal B$-calculus

Autor:	Gomilko, Alexander, Tomilov, Yuri
Rok vydání:	2024
Předmět:	Mathematics - Functional Analysis Mathematics - Analysis of PDEs Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	We improve the classical results by Brenner and Thom\'ee on rational approximations of operator semigroups. In the setting of Hilbert spaces, we introduce a finer regularity scale for initial data, provide sharper stability estimates, and obtain optimal approximation rates. Moreover, we strengthen a result due to Egert-Rozendaal on subdiagonal Pad\'e approximations of operator semigroups. Our approach is direct and based on the theory of the $\mathcal B$- functional calculus developed recently. On the way, we elaborate a new and simple approach to construction of the $\mathcal B$-calculus thus making the paper essentially self-contai Comment: This is a version of the paper to appear in Journal of Functional Analysis
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.14411 Zobrazit plný text záznamu View this record from Arxiv