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INTEGRAL KERNEL OPERATORS ON REGULAR GENERALIZED WHITE NOISE FUNCTIONS
Ji, Un-Cig Korean Mathematical Society 2000 대한수학회보 Vol.37 No.3
Let (and $g^*$) be the space of regular test (and generalized, resp.) white noise functions. The integral kernel operators acting on and transformation groups of operators on are studied, and then every integral kernel operator acting on can be extended to continuous linear operator on $g^*$. The existence and uniqueness of solutions of Cauchy problems associated with certain integral kernel operators with intial data in $g^*$ are investigated.
YEH CONVOLUTION OF WHITE NOISE FUNCTIONALS
Ji, Un Cig,Kim, Young Yi,Park, Yoon Jung The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.5
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.
ON A q-FOCK SPACE AND ITS UNITARY DECOMPOSITION
Ji, Un-Cig,Kim, Young-Yi Korean Mathematical Society 2006 대한수학회보 Vol.43 No.1
A Fock representation of q-commutation relation is studied by constructing a q-Fock space as the space of the representation, the q-creation and q-annihilation operators (-1 < q < 1). In the case of 0 < q < 1, the q-Fock space is interpolated between the Boson Fock space and the full Fock space. Also, a unitary decomposition of the q-Fock space $(q\;{\neq}\;0)$ is studied.
QUANTUM EXTENSIONS OF FOURIER-GAUSS AND FOURIER-MEHLER TRANSFORMS
Ji, Un-Cig Korean Mathematical Society 2008 대한수학회지 Vol.45 No.6
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.
Unitary multiplier and dilation of projective isometric representation
Ji, Un Cig,Kim, Young Yi,Park, Su Hyung Elsevier 2007 Journal of mathematical analysis and applications Vol.336 No.1
<P><B>Abstract</B></P><P>In this paper we study unitary operator-valued multiplier <I>σ</I> on a normal subsemigroup <I>S</I> of a group <I>G</I> with its extension to <I>G</I>. A dilation of a projective isometric <I>σ</I>-representations of <I>S</I> to a projective unitary Φ(σ)-representation of <I>G</I> is established for a suitable unitary operator-valued multiplier Φ(σ) associated with the multiplier <I>σ</I> which is explicitly constructed during the study.</P>