Optimal error estimates in operator-norm approximations of semigroups

被引：13
|
作者：
Bentkus, V
Paulauskas, V
机构：
[1] Vilnius Pedag Univ, Dept Math, LT-2004 Vilnius, Lithuania
[2] Vilnius State Univ, Dept Math & Informat, LT-03225 Vilnius, Lithuania
[3] Inst Math & Informat, Vilnius, Lithuania
来源：
LETTERS IN MATHEMATICAL PHYSICS | 2004年 / 68卷 / 03期
关键词：
Chernoff theory; Euler approximations; Trotter-Kato formula; holomorphic semigroups; Ritt condition;
D O I：
10.1023/B:MATH.0000045552.97035.87
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We demonstrate that an idea related to the Central Limit Theorem and approximations by accompanying laws in probability theory is useful to get optimal convergence rates in some approximation formulas for operators. As examples we provide a bound for Euler approximations of bounded holomorphic semigroups; a bound for error in approximation of a power of operators by accompanying exponents, which is a useful tool in analysis of the Trotter-Kato formula, and can be considered as an extended version of Chernoffs 'rootn-lemma'.
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页码：131 / 138
页数：8
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