Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2011; 48(2): 291-302

Printed March 1, 2011

https://doi.org/10.4134/BKMS.2011.48.2.291

Copyright © The Korean Mathematical Society.

Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms

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