Self-adjointness of some infinite-dimensional elliptic operators and application to stochastic quantization
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We consider an operator K˚ϕ = Lϕ−: <CDU(x), Dϕ> in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, U∈W 1,4(H, μ) and μ is the invariant measure associated with L. We show that K˚ is essentially self-adjoint in the space L 2(H, ν) where ν is the “Gibbs” measure ν(dx) = Z −:1 e −:2U(x) dx. An application to Stochastic quantization is given.
Key wordsEssential self-adjointness Stochastic partial differential equations Stochastic quantization
Mathematics Subject Classification (2000)47B25 60H15 81S20
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