Rational approximation of holomorphic semigroups revisited
C. J. K. Batty, A. M. Gomilko, Yuri Tomilov · Journal of the London Mathematical Society · 2025
Abstract Using a recently developed ‐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.