Integral transforms, convolution products, and first variations (Q1774683)

\textit{Y.-J. Lee} [J. Funct. Anal. 47, 153--164 (1982; Zbl 0487.44006)] defined an integral transform of analytic functionals on abstract Wiener space. The Fourier-Wiener transform, the Fourier-Feynman transform, and the Gauss transform are special cases of the integral transform. \textit{K. S. Chang, B. S. Kim} and \textit{I. Yoo} [Numer. Funct. Anal. Optimization 21, No. 1/2, 97--105 (2000; Zbl 0948.28008)] established an interesting relationship between the integral transform and the convolution product for functionals on an abstract Wiener space. In this paper, the authors establish the various relationships that exist among the integral transform, the convolution product, and the first variation.