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An operator-theoretic proof of an estimate on the transfer operator. (English) Zbl 0946.47026
The authors address the question: How fast the Trotter-Kato type product formula \[ [\exp(tV/2n)\exp(-t\Delta/n)\exp(tV/2n)]^n \] converges to \(\exp\{(-\Delta +V)\}\)? Here \(\Delta\) is a Laplacian on \(R^N\) and \(V\) is a potential. Using operator techniques they prove a fine estimate in terms of \(L^2\)-operator norm convergence and some smoothness conditions on \(V\). Similar estimations were obtained by T. Ichinose and S. Takanobu [Nagoya Math. J. 149, 53-81 (1998; Zbl 0917.47041)] using probabilistic methods.

47D06 One-parameter semigroups and linear evolution equations
47D08 Schrödinger and Feynman-Kac semigroups
Full Text: DOI
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