@article{EJP61,
author = {Takashi Ichinose and Satoshi Takanobu},
title = {The Norm Estimate of the Difference Between the Kac Operator and Schrödinger Semigroup II: The General Case Including the Relativistic Case},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {5},
year = {2000},
keywords = {Schrödinger operator, Schrödinger semigroup, relativistic Schrödinger operator, Trotter product formula, Lie-Trotter-Kato product formula, Feynman-Kac formula, subordinationof Brownian motion, Kato's inequality},
abstract = {More thorough results than in our previous paper in Nagoya Math. J. are given on the $L_p$-operator norm estimates for the Kac operator $e^{-tV/2} e^{-tH_0} e^{-tV/2}$ compared with the Schrödinger semigroup $e^{-t(H_0+V)}$. The Schrödinger operators $H_0+V$ to be treated in this paper are more general ones associated with the Lévy process, including the relativistic Schrödinger operator. The method of proof is probabilistic based on the Feynman-Kac formula. It differs from our previous work in the point of using the Feynman-Kac formula not directly for these operators, but instead through subordination from the Brownian motion, which enables us to deal with all these operators in a unified way. As an application of such estimates the Trotter product formula in the $L_p$-operator norm, with error bounds, for these Schrödinger semigroups is also derived.},
pages = {no. 5, 1-47},
issn = {1083-6489},
doi = {10.1214/EJP.v5-61},
url = {http://ejp.ejpecp.org/article/view/61}}