International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 591-608
doi:10.1155/S0161171202006361

Relationships of convolution products, generalized transforms 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.