Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms
Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 291-302
https://doi.org/10.4134/BKMS.2011.48.2.291
Printed March 1, 2011
Man Kyu Im, Un Cig Ji, and Yoon Jung Park
Hannam University, Chungbuk NationalUniversity, Chungbuk National University
Abstract : We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification $\mathcal{B}_{\bf C}$ of an abstract Wiener space $(\mathcal{H},\mathcal{B},\nu)$. Secondly, we introduce a new class of convolution products of functionals defined on $\mathcal{B}_{\bf C}$ 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
MSC numbers : 28C20; Secondary 44A20, 44A35
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