The Behavior of the First Variation Under the Fourier-Feynman Transform on Abstract Wiener Spaces

Abstract

We construct the behavior of the first variation under the Fourier-Feynman transform and we show that theWiener integral of the first variation can be nicely behaved under the Fourier-Feynman transform for functionals F(x) = ∫_H exp{i (h, x)~} dμ(h) in the Fresnel class and the Fourier-Feynman transform of the first variation can be perfectly expressed as the limit of Wiener integrals of the first variation on the abstract Wiener space.