The error estimate of the integral kernel for the Trotter product
formula for Schrödinger operators is shown. A basic tool for doing so is
the Feynman-Kac formula based on the pinned Brownian motion. This formula
enables us to express the integral kernel in handleable form and hence estimate
it. As a consequence the Trotter product formula in the $L_p$ operator norm is
obtained.
Publié le : 1997-10-14
Classification:
Trotter product formula in the kernel level,
Trotter product formula in $L_p$-operator norm,
Feynman-Kac formula,
60H30,
60H10,
60J35,
60J65
@article{1023481116,
author = {Takanobu, Satoshi},
title = {On the error estimate of the integral kernel for the Trotter
product formula for Schr\"odinger operators},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1895-1952},
language = {en},
url = {http://dml.mathdoc.fr/item/1023481116}
}
Takanobu, Satoshi. On the error estimate of the integral kernel for the Trotter
product formula for Schrödinger operators. Ann. Probab., Tome 25 (1997) no. 4, pp. 1895-1952. http://gdmltest.u-ga.fr/item/1023481116/