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

Relationships among transforms, convolutions, and first variations

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

Received 7 October 1997

Copyright © 1999 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.

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).