Quantum Laplacians on generalized operators on boson fock space

• Autorzy: Accardi L. , Barhoumi A. , Ji U. C.
• Języki publikacji: EN

Abstrakty

EN

By adapting the white noise theory, the quantum analogues of the (classical) Gross Laplacian and Lévy Laplacian, so called the quantum Gross Laplacian and quantum Lévy Laplacian, respectively, are introduced as the Laplacians acting on the spaces of generalized operators. Then the integral representations of the quantum Laplacians in terms of quantum white noise derivatives are studied. Correspondences of the classical Laplacians and quantum Laplacians are studied. The solutions of heat equations associated with the quantum Laplacians are obtained from a normal-ordered white noise differential equation.

Słowa kluczowe

EN

Fock space; generalized operator; heat equation; operator symbol; quantum Gross Laplacian; quantum Lévy Laplacian; quantum white noise

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2011
• Tom: Vol. 31, Fasc. 2
• Strony: 203--225
• Opis fizyczny: Bibliogr. 41 poz.,

Twórcy

autor

Accardi L.

• Centro Vito Volterra Facultà di Economica, Università di Tor Vergata, Via di Tor Vergata, 00133 Roma, Italy

autor

Barhoumi A.

• Department of Mathematics, Higher School of Sciences and Technologies of Hammam-Sousse, Sousse University, Tunisia

autor

Ji U. C.

• Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763, Korea

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