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A QUANTUM APPROACH TO LAPLACE OPERATORS

LUIGI ACCARDI

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

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ABDESSATAR BARHOUMI

Nabeul Preparatory Engineering Institute, Mrezgua University Compus, 8000 Nabeul, Tunisia

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, and

HABIB OUERDIANE

Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, 1060 Tunis, Tunisia

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https://doi.org/10.1142/S0219025706002329Cited by:14 (Source: Crossref)

Abstract

In this paper, a theory of stochastic processes generated by quantum extensions of Laplacians is developed. Representations of the associated heat semigroups are discussed by means of suitable time shifts. In particular the quantum Brownian motion associated to the Lévy–Laplacian is obtained as the usual Volterra–Gross Laplacian using the Cesàro Hilbert space as initial space of our process as well as multiplicity space of the associated white noise.

Keywords:

AMSC: primary: 60J65, secondary: 60J45, secondary: 60H40

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