Rational approximation of holomorphic semigroups revisited
<|reference_start|>Rational approximation of holomorphic semigroups revisited: Using a recently developed $\mathcal H$-calculus we propose a unified approach to the study of rational approximations of holomorphic semigroups on Banach spaces. We provide unified and simple proofs to a number of basic results on semigroup approximations and substantially improve some of them. We show that many of our estimates are essentially optimal, thus complementing the existing literature.<|reference_end|>
@article{batty2024rational,
    title={Rational approximation of holomorphic semigroups revisited},
    author={Charles Batty, Alexander Gomilko, and Yuri Tomilov},
    journal={arXiv preprint arXiv:2403.15894},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.15894},
    primaryClass={math.FA cs.NA math.AP math.NA}
}