Division of Mathematics
Graduate School of Information Sciences
Tohoku University

Information Mathematical Sciences Colloquium

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Speaker: Un Cig Ji (Department of Mathematics, Chungbuk National University, Korea)
Title: Noncommutative Extensions of Fourier-Gauss and Fourier-Mehler Transforms
Time: 18 April 2007, 16:00-17:00
(Tea and snack will be served before the lecture)
Place: 2nd floor Large Lecture Room, GSIS-building at Aobayama Campus, Tohoku Univ.
abstract:
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. The irreducibility of the canonical commutation relation for operator acting on a space of operators in Boson Fock space is proved and then a characterization of the quantum Fourier-Mehler transform is studied.

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