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The Feynman integral of quadratic potentials depending on two time variables. (English) Zbl 0594.28013
Summary: We show that the double integral of certain quadratic potentials depending on two time variables is in a Banach algebra \({\mathcal S}\) of functions on Wiener space all of whose members have an analytic Feynman integral. Corollaries are given insuring (a) that \({\mathcal S}\) 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.

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
81S40 Path integrals in quantum mechanics
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