• Title/Summary/Keyword: Fourier-Mehler transform

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QUANTUM EXTENSIONS OF FOURIER-GAUSS AND FOURIER-MEHLER TRANSFORMS

  • Ji, Un-Cig
    • 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.

YEH CONVOLUTION OF WHITE NOISE FUNCTIONALS

  • Ji, Un Cig;Kim, Young Yi;Park, Yoon Jung
    • 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.

CONVOLUTIONS OF WHITE NOISE OPERATORS

  • Ji, Un-Cig;Kim, Young-Yi
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.5
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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.