RELATIONS AMONG THE FIRST VARIATION, THE CONVOLUTIONS AND THE GENERALIZED FOURIER-GAUSS TRANSFORMS

Abstract

We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification <TEX>$\cal{B}_C$</TEX> of an abstract Wiener space (<TEX>$\cal{H}$</TEX>, <TEX>$\cal{B}$</TEX>, <TEX>${\nu}$</TEX>). Secondly, we introduce a new class of convolution products of functionals defined on <TEX>$\cal{B}_C$</TEX> and study several properties of the convolutions. Then we study various relations among the first variation the convolutions, and the generalized Fourier-Gauss transforms.