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Rational approximation of holomorphic semigroups revisited (2403.15894v1)
Published 23 Mar 2024 in math.FA, cs.NA, math.AP, and math.NA
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.