Self-adjointness of some infinite-dimensional elliptic operators and application to stochastic quantization

We consider an operator K˚ϕ = Lϕ−: in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, U∈W1,4(H, μ) and μ is the invariant measure associated with L. We show that K˚ is essentially self-adjoint in the space L2(H, ν) where ν is the “Gibbs” measure ν(dx) = Z−:1e−:2U(x)dx. An application...

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Bibliographic Details
Published in:Probability theory and related fields 2000-09, Vol.118 (1), p.131-145
Main Authors: DA PRATO, Giuseppe, TUBARO, Luciano
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Functional analytical methods
Hilbert space
Mathematical analysis
Mathematics
Measurement
Operator theory
Physics
Probability
Probability and statistics
Probability theory and stochastic processes
Quantum mechanics
Sciences and techniques of general use
Stochastic analysis
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Summary:We consider an operator K˚ϕ = Lϕ−: in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, U∈W1,4(H, μ) and μ is the invariant measure associated with L. We show that K˚ is essentially self-adjoint in the space L2(H, ν) where ν is the “Gibbs” measure ν(dx) = Z−:1e−:2U(x)dx. An application to Stochastic quantization is given.
ISSN:0178-8051
1432-2064
DOI:10.1007/pl00008739