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arXiv · 2403.15894

Rational approximation of holomorphic semigroups revisited

Charles Batty·Alexander Gomilko·Yuri Tomilov
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Abstract

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.

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Charles Batty, Alexander Gomilko, Yuri Tomilov. 2024-03-23. Rational approximation of holomorphic semigroups revisited. https://arxiv.org/abs/2403.15894

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