Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space

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概要

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• The spectra of the quadratic Hamiltonians on the two-dimensional Euclidean space are determined completely by using the theory of the metaplectic representation. In some cases, the corresponding heat kernels are studied in connection with the well-definedness of the Wiener integrations. A proof of the Lévy formula for the stochastic area and a relation between the real and complex Hermite polynomials are given in our framework.

• 社団法人 日本数学会の論文
• 2000-04-00

著者

• Matsumoto Hiroyuki

  School Of Informatics And Sciences Nagoya University

• Ueki Naomasa

  Department of Mathematics, Faculty of Science Himeji Institute of Technology

関連論文

• Some Absolute Continuity Relationships for Certain Anticipative Transformations of Geometric Brownian Motions
• An analogue of Pitman's 2M-X theorem for exponential Wiener functionals, Part I : A time-inversion approach
• An analogue of Pitman's 2M-X theorem for exponential Wiener functionals : Part II: The role of the generalized inverse Gaussian laws
• Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space

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