International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 191-204
doi:10.1155/S0161171299221916

Relationships among transforms, convolutions, and first variations

Jeong Gyoo Kim,1 Jung Won Ko,1 Chull Park,2 and David Skoug3

1Department of Mathematics, Yonsei University, Seoul 120-749, Korea
2Department of Mathematics and Statistics, Miami University, Oxford 45056, OH, USA
3Department of Mathematics and Statistics, University of Nebraska, Lincoln 68588, NE, USA

Received 7 October 1997

Copyright © 1999 Jeong Gyoo Kim et al. 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.

Abstract

In this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionals F on Wiener space of the form F(x)=f(〈α1,x〉,…,〈αn,x〉),                                                      (*) where 〈αj,x〉 denotes the Paley-Wiener-Zygmund stochastic integral ∫0Tαj(t)dx(t).