Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class F-A1,F-A2 than the Fresnel class F(B) which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space having the form F(x) = G(x)Psi(((e) over right arrow ,x)(similar to)), where G is an element of F(B) and Psi = psi + phi with psi is an element of L-1(R-n) and phi is the Fourier transform of a complex Borel measure of bounded variation on R-n. We also prove a translation theorem for the analytic Feynman integral of the above functionals.