On rates in Euler's formula for C_0-semigroups
arXiv:1301.44064 citationsh-index: 19
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Provides a theoretical advance in semigroup approximation theory for mathematicians working on operator semigroups.
The paper derives optimal convergence rates for Euler's approximation of C_0-semigroups on ranges of generalized Stieltjes functions, improving upon and unifying partial results from the literature.
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.