International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 591-608
Relationships of convolution products, generalized
transforms, and the first variation on function space
Department of Mathematics, Dankook University, Cheonan 330-714, South Korea
Received 9 December 2000
Copyright © 2002 Seung Jun Chang and Jae Gil Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
. These results subsume similar known results obtained by
Park, Skoug, and Storvick (1998) for the standard Wiener process.