STRONG UNIQUENESS FOR CERTAIN INFINITE DIMENSIONAL

DIRICHLET OPERATORS AND APPLICATIONS TO STOCHASTIC QUANTIZATION

VITALI LISKEVICH AND MICHAEL RÖCKNER

Abstract. Strong and Markov uniqueness problems in L^{2} for Dirichlet operators on rigged Hilbert spaces are studied. An analytic approach based on a–priori estimates is used. The extension of the problem to the L^{p}-setting is discussed. As a direct application essential self–adjointness and strong uniqueness in L^{p} is proved for the generator (with initial domain the bounded smooth cylinder functions) of the stochastic quantization process for Euclidean quantum field theory in finite volume Λ ⊂ ℝ^{2}.