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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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