FAJan 18, 2013
On rates in Euler's formula for C_0-semigroupsAlexander Gomilko, Yuri Tomilov
By functional calculus methods, we obtain optimal convergence rates in Euler's approximation formula for C_0-semigroups restricted to ranges of generalized Stieltjes functions. Our results include a number of partial cases studied in the literature and cannot essentially be improved.