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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.

MSC:
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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