Integral transform and convolution of analytic functionals on abstract Wiener space

Yeh defined a convolution of functionals on classical Wiener space and investigated the relationship between the Fourier-Wiener transforms of functionals in certain classes and the Fourier-Wiener transform of their convolution. Yoo extended Yeh's results to abstract Wiener space. In this paper, we introduce the integral transform and convolution of analytic functionals on abstract Wiener space. And we establish the relationship between the integral transforms of exponential type of analytic functionals and the integral transform of their convolution. Also we obtain Parseval's and Plancherel's relations for those functionals from this relationship. The main results of Yeh and Yoo then follow from our results as corollaries.