Journal of the
Korean Mathematical Society JKMS

In this paper, we define the conditional first variation over Wiener paths in abstract Wiener space and investigate its properties. Using these properties, we also investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transforms of functions in a Banach algebra which is equivalent to the Fresnel class. Finally, we provide another method evaluating the Fourier-Feynman transform for the product of a function in the Banach algebra with $n$ linear factors.

Keywords: conditional first variation, conditional Fourier-Feynman transform, first variation, Fourier-Feynman transform, Fresnel class, Wiener paths in abstract Wiener space

MSC numbers: 28C20