• 대한수학회지
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• 제45권6호
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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.

• 충청수학회지
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• 제23권1호
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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 applied mathematics & informatics
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• 제31권5_6호
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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.

• 대한수학회보
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• 제48권5호
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• pp.1003-1014
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• 2011

Motivated by the convolution product of white noise functionals, we introduce a new notion of convolution products of white noise operators. Then we study several interesting relations between the convolution products and the quantum generalized Fourier-Mehler transforms, and study a quantum-classical correspondence.