Rational approximation of operator semigroups via the $\mathcal B$-calculus
<|reference_start|>Rational approximation of operator semigroups via the $\mathcal B$-calculus: 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<|reference_end|>
@article{gomilko2024rational,
    title={Rational approximation of operator semigroups via the $\mathcal
  B$-calculus},
    author={Alexander Gomilko and Yuri Tomilov},
    journal={arXiv preprint arXiv:2403.14411},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.14411},
    primaryClass={math.FA cs.NA math.AP math.NA}
}