Simon B.
A Feynman-Kac Formula for Unbounded Semigroups
(12K, LaTeX)

ABSTRACT.  We prove a Feynman-Kac formula for Schr\"odinger 
operators with potentials $V(x)$ that obey (for 
all $\varepsilon >0$) 
\[
V(x) \geq -\varepsilon |x|^2 - C_\varepsilon.
\]
Even though $e^{-tH}$ is an unbounded operator, any 
$\varphi, \psi \in L^2$ with compact support lie in 
$D(e^{-tH})$ and $\langle \varphi, e^{-tH}\psi\rangle$ 
is given by a Feynman-Kac formula.