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

Valentin Zagrebnov (1)

1 I2M - Institut de Mathématiques de Marseille

The paper improves approximation theory based on the Trotter-Kato product formulae. For self-adjoint C0-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 K2.

Mots clés: Strongly continuous semigroup; Chernoff approximation formula; Trotter-Kato product formulae

Domaines: Analyse fonctionnelle [math.FA]

Valentin Zagrebnov. Approximations of self-adjoint \(C_0\)-semigroups in the operator-norm topology. Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 2020, 73, ⟨10.17951/a.2019.73.2.175-194⟩. ⟨hal-03662025⟩