• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.1-10
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• 2010

In this note, we investigate the infinitesimal generators of the transformation groups induced by the Fourier-Gauss and Fourier-Mehler transforms on white noise functionals.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1785-1801
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• 2008

Noncommutative extensions of the Gross and Beltrami Laplacians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Fourier- Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.291-302
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• 2011

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.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.825-834
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• 2013

In this paper, we study the Yeh convolution of white noise functionals. We first introduce the notion of Yeh convolution of test white noise functionals and prove a dual property of the Yeh convolution. By applying the dual object of the Yeh convolution, we study the Yeh convolution of generalized white noise functionals, which is a non-trivial extension. Finally, we study relations between the Yeh convolution and Fourier-Gauss, Fourier-Mehler transform.