Fourier-Feynman transforms for functionals in a generalized fresnel class

Huffman, Park and Skoug introduced various results for the L_p analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra S introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class F_A1,A2 containing F(B). In this paper, we establish various interesting relationships and expressions involving the first variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in F_A1,A2.