TY - JOUR
T1 - Essential self-adjointness of Dirichlet operators on a path space with Gibbs measures via an SPDE approach
AU - Kawabi, Hiroshi
AU - Röckner, Michael
N1 - Funding Information:
This work was begun while the first author was at University of Bielefeld in fall 2004 and was mostly done while he was at University of Bonn in spring 2005. He would like to thank both universities (in particular Professor Sergio Albeverio) for warm hospitalities. He was supported by the Research Fellowships of the Japan Society for Promotion of Science for Young Scientists and is supported by 21st century COE program “Development of Dynamic Mathematics with High Functionality” at Faculty of Mathematics, Kyushu University. Financial support of the DFG-Research Group “Spectral Analysis, Asymptotic Distributions and Stochastic Dynamics” and the BiBoS-Research Centre is also gratefully acknowledged.
PY - 2007/1/15
Y1 - 2007/1/15
N2 - 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.
AB - 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.
KW - Dirichlet operator
KW - Essential self-adjointness
KW - Gibbs measure
KW - Infinite volume path space
KW - P (φ{symbol})-Quantum fields
KW - SPDE
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U2 - 10.1016/j.jfa.2006.06.017
DO - 10.1016/j.jfa.2006.06.017
M3 - Article
AN - SCOPUS:33750936767
SN - 0022-1236
VL - 242
SP - 486
EP - 518
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -