Probability Theory and Related Fields

, Volume 118, Issue 1, pp 131–145 | Cite as

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

  • Giuseppe Da Prato
  • Luciano Tubaro


We consider an operator ϕ = Lϕ−: <CDU(x), Dϕ> in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, UW 1,4(H, μ) and μ is the invariant measure associated with L. We show that 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 words

Essential self-adjointness Stochastic partial differential equations Stochastic quantization 

Mathematics Subject Classification (2000)

47B25 60H15 81S20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Giuseppe Da Prato
    • 1
  • Luciano Tubaro
    • 2
  1. 1.Dipartimento di MatematicaScuola Normale Superiore di PisaPisaItaly
  2. 2.Department of MathematicsUniversity of TrentoTrentoItaly

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