Fourier-feynman transform, convolution and first variation of functional on abstract wiener

Park, Skoug and Storvick examined various relationships among the first variation, the Fourier-Feynman tranform, and the convolution product for functionals, on classical Wiener space(C o[0,1],m), which belong to some Banach algebra S.In this paper, we extend the above concepts to an abstract Wiener space(B,ν)and the first variation for functionals in the Fresnel Class F(B)which corresponds to S. Since the Fresnel class F(B)is the abstracat Wiener space setting of the Banach algebra S, our result inclued the above results as special cases