Essential self-adjointness of Dirichlet operators on a path space with Gibbs measures via an SPDE approach

Hiroshi Kawabi, Michael Röckner

Research output: Contribution to journalArticle

5 Citations (Scopus)


The main objective of this paper is to prove the essential self-adjointness of Dirichlet operators in L2 (μ) where μ is a Gibbs measure on an infinite volume path space C (R, Rd). This operator can be regarded as a perturbation of the Ornstein-Uhlenbeck operator by a nonlinearity and corresponds to a parabolic stochastic partial differential equation (= SPDE, in abbreviation) on R. In view of quantum field theory, the solution of this SPDE is called a P (φ{symbol})1-time evolution.

Original languageEnglish
Pages (from-to)486-518
Number of pages33
JournalJournal of Functional Analysis
Issue number2
Publication statusPublished - 2007 Jan 15
Externally publishedYes



  • Dirichlet operator
  • Essential self-adjointness
  • Gibbs measure
  • Infinite volume path space
  • P (φ{symbol})-Quantum fields
  • SPDE

ASJC Scopus subject areas

  • Analysis

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