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http://dx.doi.org/10.4134/BKMS.2011.48.2.291

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

Im, Man-Kyu (Department of Mathematics Hannam University)
Ji, Un-Cig (Department of Mathematics Research institute of Mathematical Finance Chungbuk National University)
Park, Yoon-Jung (Department of Mathematics Chungbuk National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 291-302 More about this Journal
Abstract
We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification $\cal{B}_C$ of an abstract Wiener space ($\cal{H}$, $\cal{B}$, ${\nu}$). Secondly, we introduce a new class of convolution products of functionals defined on $\cal{B}_C$ 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;
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