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 Kim1 , Jung Won Ko1 , Chull Park3 and David Skoug4

1Department of Mathematics, Yonsei University, Seoul 120-749, Korea
 3Department of Mathematics and Statistics, Miami University, Oxford 45056, OH, USA
 4Department of Mathematics and Statistics, University of Nebraska, Lincoln 68588, NE, USA

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).