A QUANTUM APPROACH TO LAPLACE OPERATORS

DOI10.1142/S0219025706002329zbMath1097.60065MaRDI QIDQ5483409

Luigi Accardi, Abdessatar Barhoumi, Habib Ouerdiane

Publication date: 14 August 2006

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

distributionWiener processLie algebrawhite noiseGel'fand tripleMarkovian semigroupquantum shiftquantum LaplacianCesàro Hilbert spaceCesàro scalar productquantum heat flowquantum Lévy Brownian motion

Mathematics Subject Classification ID

Brownian motion (60J65) Probabilistic potential theory (60J45) White noise theory (60H40)

Related Items (11)

A SIMILARITY BETWEEN THE GROSS LAPLACIAN AND THE LÉVY LAPLACIAN ⋮ Laplacian with respect to a measure on a Riemannian manifold and the Dirichlet problem. I ⋮ EXOTIC LAPLACIANS AND DERIVATIVES OF WHITE NOISE ⋮ White noise delta functions and infinite-dimensional Laplacians ⋮ Relationships between usual and exotic Hida–Kubo–Takenaka spaces ⋮ Laplacian with respect to a measure on a Hilbert space and an \(L_2\)-version of the Dirichlet problem for the Poisson equation ⋮ STOCHASTIC HEAT EQUATION ON ALGEBRA OF GENERALIZED FUNCTIONS ⋮ Higher order multi-dimensional extensions of Cesàro theorem ⋮ White noise quantum time shifts ⋮ EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES ⋮ THE EXOTIC (HIGHER ORDER LÉVY) LAPLACIANS GENERATE THE MARKOV PROCESSES GIVEN BY DISTRIBUTION DERIVATIVES OF WHITE NOISE

Cites Work

• Unnamed Item
• Structure of Markov cocycles on Fock space
• Brownian motion of a quantum harmonic oscillator
• White noise calculus and Fock space
• A duality theorem between spaces of holomorphic functions of exponential growth
• A C₀-Group Generated by the Lévy Laplacian II
• A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups
• DIAGONALIZATION OF THE LÉVY LAPLACIAN AND RELATED STABLE PROCESSES

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