The Feynman integral of quadratic potentials depending on two time variables

Abstract

We show that the double integral of certain quadratic potentials depending on two time variables is in a Banach algebra Sf of functions on Wiener space all of whose members have an analytic Feynman integral. Corollaries are given insuring (a) that S? contains a rather broad class of functions involving double integrals of potentials depending on two time parameters, and (b) the existence of the Fresnel integral for such functions.