International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 29 |Article ID 159548 | 18 pages |

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

Received09 Dec 2000


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.

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.

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