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Self-adjointness of some infinite-dimensional elliptic operators and application to stochastic quantization
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  • Published: 12 February 2014

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

  • Giuseppe Da Prato1 &
  • Luciano Tubaro2 

Probability Theory and Related Fields volume 118, pages 131–145 (2000)Cite this article

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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Authors and Affiliations

  1. Dipartimento di Matematica, Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 56126 Pisa, Italy., Italy

    Giuseppe Da Prato

  2. Department of Mathematics, University of Trento, Italy., Italy

    Luciano Tubaro

Authors
  1. Giuseppe Da Prato
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  2. Luciano Tubaro
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Additional information

Received: 13 August 1998 / Revised version: 20 September 1999 / Published online: 8 August 2000

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Cite this article

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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  • Published: 12 February 2014

  • Issue Date: September 2000

  • DOI: https://doi.org/10.1007/PL00008739

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Keywords

  • Invariant Measure
  • Elliptic Operator
  • Dirichlet Form
  • Stochastic Quantization
  • Transition Semigroup
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