An operator-theoretic proof of an estimate on the transfer operator
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 \textit{T. Ichinose} and \textit{S. Takanobu} [Nagoya Math. J. 149, 53-81 (1998; Zbl 0917.47041)] using probabilistic methods.
scientific article; zbMATH DE number 1319962