Trotter product formula and linear evolution equations on Hilbert spaces On the occasion of the 100th birthday of Tosio Kato

Abstract : The paper is devoted to evolution equations of the form ∂ ∂t u(t) = −(A + B(t))u(t), t ∈ I = [0, T ], on separable Hilbert spaces where A is a non-negative self-adjoint operator and B(·) is family of non-negative self-adjoint operators such that dom(A α) ⊆ dom(B(t)) for some α ∈ [0, 1) and the map A −α B(·)A −α is Hölder continuous with the Hölder exponent β ∈ (0, 1). It is shown that the solution operator U(t, s) of the evolution equation can be approximated in the operator norm by a combination of semigroups generated by A and B(t) provided the condition β > 2α − 1 is satisfied. The convergence rate for the approximation is given by the Hölder exponent β. The result is proved using the evolution semigroup approach.
Type de document :
Pré-publication, Document de travail
2019
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https://hal.archives-ouvertes.fr/hal-01971610
Contributeur : Valentin Zagrebnov <>
Soumis le : lundi 7 janvier 2019 - 11:21:17
Dernière modification le : mercredi 9 janvier 2019 - 01:22:46

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  • HAL Id : hal-01971610, version 1
  • ARXIV : 1901.02205

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Hagen Neidhardt, Artur Stephan, Valentin Zagrebnov. Trotter product formula and linear evolution equations on Hilbert spaces On the occasion of the 100th birthday of Tosio Kato. 2019. 〈hal-01971610〉

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