Approximations of self-adjoint \(C_0\)-semigroups in the operator-norm topology

Valentin Zagrebnov

Abstract


The paper improves approximation theory based on the Trotter–Kato product formulae. For self-adjoint \(C_0\)-semigroups we develop a lifting of the strongly convergent Chernoff approximation (or product) formula to convergence in the operator-norm topology. This allows to obtain optimal estimate for the rate of operator-norm convergence of Trotter–Kato product formulae for Kato functions from the class \(K_2\).

Keywords


Strongly continuous semigroup; Chernoff approximation formula; Trotter–Kato product formulae

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References


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DOI: http://dx.doi.org/10.17951/a.2019.73.2.175-194
Date of publication: 2020-01-16 07:29:37
Date of submission: 2020-01-04 21:27:26


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