Stabilizations of the Trotter-kato Theorem and the Chernoff Product Formula
نویسندگان
چکیده
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.
منابع مشابه
Central Limit Theorem for Products of Random Matrices
Using the semigroup product formula of P. Chernoff, a central limit theorem is derived for products of random matrices. Applications are presented for representations of solutions to linear systems of stochastic differential equations, and to the corresponding partial differential evolution equations. Included is a discussion of stochastic semigroups, and a stochastic version of the Lie-Trotter...
متن کاملNote on the Paper "the Norm Convergence of the Trotter{kato Product Formula with Error Bound" by Ichinose and Tamura
The norm convergence of the Trotter{Kato product formula is established with ultimate optimal error bound for the self-adjoint semigroup generated by the operator sum of two self-adjoint operators. A generalization is also given to the operator sum of several self-adjoint operators.
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.
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 کاملA pr 2 00 4 Note on a product formula for unitary groups
For any nonnegative self-adjoint operators A and B in a separable Hilbert space, we show that the Trotter-type formula [(ei2tA/n + ei2tB/n)/2]n converges strongly in dom(A1/2) ∩ dom(B1/2) for some subsequence and for almost every t ∈ R. This result extends to the degenerate case and to Katofunctions following the method of Kato [6]. In a famous paper [6], T. Kato proved that for any nonnegative...
متن کامل