A Feynman-Kac Formula for Unbounded Semigroups
Abstract
Description
We prove a Feynman-Kac formula for Schrodinger operators with potentials V(x) that obey (for all ε> 0): V(x) \geq - ε|x|^2 - C_ε. Even though e^{-tH} is an unbounded operator, any ϕ, ψ\in L^2 with compact support lie in D(e^{-tH}) and <ϕ, e^{-tH}ψ> is given by a Feynman-Kac formula.
5 pages, LaTeX. To appear in Proc. Intl. Conf. on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Leipzig 1999
5 pages, LaTeX. To appear in Proc. Intl. Conf. on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Leipzig 1999