Let

be the Fresnel class on an abstract Wiener space (B, H,

) which consists of functionals F of the form :

where

is a stochastic inner product between H and B, and

is in

, the space of all complex-valued countably additive Borel measures on H. We introduce the concepts of an

analytic Fourier-Feynman transform (

) and a convolution product on

and verify the existence of the

analytic Fourier-Feynman transforms for functionls in

. Moreover, we verify that the Fresnel class

is closed under the

analytic Fourier-Feynman transform and the convolution product, respectively. And we investigate some interesting properties for the

-repeated

analytic Fourier-Feynman transform on

. Finally, we show that several results in [9] come from our results in Section 3.