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

Title & Authors
RELATIONS AMONG THE FIRST VARIATION, THE CONVOLUTIONS AND THE GENERALIZED FOURIER-GAUSS TRANSFORMS
Im, Man-Kyu; Ji, Un-Cig; Park, Yoon-Jung;

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