Abstract
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.
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Received: 13 August 1998 / Revised version: 20 September 1999 / Published online: 8 August 2000
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Da Prato, G., Tubaro, L. Self-adjointness of some infinite-dimensional elliptic operators and application to stochastic quantization. Probab Theory Relat Fields 118, 131–145 (2000). https://doi.org/10.1007/PL00008739
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DOI: https://doi.org/10.1007/PL00008739