Journal of the
Korean Mathematical Society JKMS

In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cyl-inder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with $n$ linear factors.

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

MSC numbers: 28C20