Journal of the
Korean Mathematical Society JKMS

In this paper we express analytic Feynman integral of the first variation of a functional $F$ in terms of analytic Feynman integral of the product of $F$ with a linear factor and obtain an integration by parts formula for the analytic Feynman integral of functionals on abstract Wiener space. We find the Fourier-Feynman transform for the product of functionals in the Fresnel class ${\mathcal F}(B)$ with $n$ linear factors.

Keywords: abstract Wiener space, Fourier-Feynman transform, first variation, integration by parts formula, Fresnel class

MSC numbers: 28C20, 44A35