منابع مشابه
The Trotter-Kato theorem and approximation of PDEs
We present formulations of the Trotter-Kato theorem for approximation of linear C0-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.
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Using the Trotter-Kato theorem we prove the convergence of the unitary dynamics generated by an increasingly singular Hamiltonian in the case of a single field coupling. The limit dynamics is a quantum stochastic evolution of Hudson-Parthasarathy type, and we establish in the process a graph limit convergence of the pre-limit Hamiltonian operators to the Chebotarev-Gregoratti-von Waldenfels Ham...
متن کاملTrotter-Kato product formula for unitary groups
Let A and B be non-negative self-adjoint operators in a separable Hilbert space such that its form sum C is densely defined. It is shown that the Trotter product formula holds for imaginary times in the L-norm, that is, one has
متن کاملStabilizations of the Trotter-kato Theorem and the Chernoff Product Formula
This paper concerns versions of the Trotter-Kato Theorem and the Chernoff Product Formula for C0-semigroups in the absence of stability. Applications to A-stable rational approximations of semigroups are presented.
متن کاملOn Error Estimates for the Trotter-kato Product Formula
We study the error bound in the operator norm topology for the Trotter exponential product formula as well as for its generalization a la Kato. In the frame of the abstract setting we give a simple proof of error estimates which improve some of recent results in this direction.
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ژورنال
عنوان ژورنال: Korean Journal of Mathematics
سال: 2013
ISSN: 1976-8605
DOI: 10.11568/kjm.2013.21.3.325