Accretive perturbations and error estimates for the Trotter product formula期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Accretive perturbations and error estimates for the Trotter product formula

Authors:

Vincent Cachia Hagen Neidhardt Valentin A Zagrebnov

Institution:

(1) Centre de Physique Théorique, CNRS-Luminy-Case 907, F-13288 Marseille Cedex 9, France;(2) Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117 Berlin, Germany;(3) Départment de Physique, Université de la Méditerranée (Aix-Marseille II), F-13288 Marseille Cedex 9, France

Abstract:

We study the operator-norm error bound estimate for the exponential Trotter product formula in the case of accretive perturbations. LetA be a semibounded from below self-adjoint operator in a separable Hilbert space. LetB be a closed maximal accretive operator such that, together withB ^*, they are Kato-small with respect toA with relative bounds less than one. We show that in this case the operator-norm error bound estimate for the exponential Trotter product formula is the same as for the self-adjointB 12]:

$\parallel (e^{ - tA/n} e^{ - tB/n} )^n - e^{ - t(A + B)} \parallel \leqslant L\frac{{\ln n}}{n},n = 2,3,....$

We verify that the operator—(A+B) generates a holomorphic contraction semigroup. One gets similar results whenB is substituted byB ^*.To the memory of Tosio Kato

Keywords:

AMS Classification" target="_blank">AMS Classification 47D03 47B25 35K22 41A80

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