  In this paper we introduce the concept of a convolution type operation of
functionals on Wiener space. It contains several kinds of the concepts of
convolution products on Wiener space, which have been studied by many authors.
We then investigate fundamental relationships between generalized analytic
Fourier--Feynman transforms and convolution type operations. Both of the
generalized analytic Fourier--Feynman transform of the convolution type
operation and the convolution type operation of the generalized analytic
Fourier--Feynman transforms are represented as a product of the generalized
analytic Fourier--Feynman transforms.
