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,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, where G∈F(B)and Ψ = ψ + φ with ψ ∈ L₁(ℝⁿ) and φ is the Fourier transform of a complex Borel measure of bounded variation on ℝⁿ. We also prove a translation theorem for the analytic Feynman integral of the above functionals.