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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 Hindawi Publishing Corporation. 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 S(Lab[0,T]). These results subsume similar known results obtained by Park, Skoug, and Storvick (1998) for the standard Wiener process.