Analytic fourier-feynman transform and convolution of functionals on abstract wiener space

Huffman, Park and Skoug obtained various results for the L_p analytic Fourier-Feynman transform and the convolution of functionals in some Banach algebra S on classical Wiener space. Recently, Ahn studied L₁ analytic Fourier-Feynman transform theory for functionals in the Fresnel class F(B) of abstract Wiener space (B, ν). In this paper we first define an L_p analytic Fourier-Feynman transform and a convolution of functionals on a product abstract Wiener space and establish various relationships between the Fourier-Feynman transform and convolution for functionals in the generalized Fresnel class F_{A1, A2} containing F(B). Also we obtain Parseval’s relation for those functionals. Results of Huffman, Park, Skoug and Ahn are corollaries of our results.