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arXiv · 2403.14411

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

Alexander Gomilko·Yuri Tomilov
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Abstract

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

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Alexander Gomilko, Yuri Tomilov. 2024-03-21. Rational approximation of operator semigroups via the $\mathcal B$-calculus. https://arxiv.org/abs/2403.14411

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