84 citations · 467 across the 54 of their papers we have counts for
59 papers
Operator-norm Trotter product formula on Banach spaces
Valentin A. Zagrebnov
In this paper we collect results concerning the {operator-norm} convergent {Trotter} product formula for two semigroups $\{\e^{- t A}\}_{t\geq 0}$, $\{\e^{- t B}\}_{t\geq 0}$, with…
Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey
Hagen Neidhardt, Artur Stephan, Valentin Zagrebnov
We give a review of results on the operator-norm convergence of the Trotter product formula on Hilbert and Banach spaces, which is focused on the problem of its convergence rates.…
Solution Operator for Non-Autonomous Perturbation of Gibbs Semigroup
Valentin Zagrebnov
The paper is devoted to a linear dynamics for non-autonomous perturbation of the Gibbs semigroup on a separable Hilbert space. It is shown that evolution family {U(t, s)} 0s$\…
Notes on the Chernoff Product Formula
Valentin Zagrebnov
We revise the strong convergent Chernoff product formula and extend it, in a Hilbert space, to convergence in the operator-norm topology. Main results deal with the self-adjoint Ch…
Trotter product formula and linear evolution equations on Hilbert spaces On the occasion of the 100th birthday of Tosio Kato
Hagen Neidhardt, Artur Stephan, Valentin Zagrebnov
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 s…
Trotter-Kato product formulae in Dixmier ideal
Valentin Zagrebnov
It is shown that for a certain class of the Kato functions the Trotter-Kato product formulae converge in Dixmier ideal C 1, in topology, which is defined by the 1,…