Optimal Error Estimates in Operator-Norm Approximations of Semigroups |
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| Authors: | Bentkus V Paulauskas V |
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| Institution: | (1) Department of Mathematics, Vilnius Pedagogical University, Studentu 39, LT2004 Vilnius, Lithuania;(2) Institute of Mathematics and Informatics, Lithuania |
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| Abstract: | 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 Chernoff's 
lemma . |
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| Keywords: | Chernoff theory Euler approximations Trotter– Kato formula holomorphic semigroups Ritt condition |
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