Relationships of convolution products, generalizedtransforms, and the first variation on function space

Abstract

We use a generalized Brownian motion process to define the generalized Fourier‐Feynman transform, the convolution product, and the first variation. We then examine the various relationships that exist among the first variation, the generalized Fourier‐Feynman transform, and the convolution product for functionals on function space that belong to a Banach algebra S(Lab[0, T]). These results subsume similar known results obtained by Park, Skoug, and Storvick (1998) for the standard Wiener process.