ANALYTIC FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FUNCTIONALS IN A GENERALIZED FRESNEL CLASS

Huffman, Park and Skoug introduced various results for the Lp 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. Moreover they introduced the Lp analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class FA1,A2 containing F(B). In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in FA1,A2 , than the above results.