Strong uniqueness for certain infinite dimensional Dirichlet operators and applications to stochastic quantization

Vitali Liskevich; Michael Röckner

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arXiv · math/9801144

Strong uniqueness for certain infinite dimensional Dirichlet operators and applications to stochastic quantization

Vitali Liskevich·Michael Röckner

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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 $Λ\subset \R^2$.

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Vitali Liskevich, Michael Röckner. 1998-01-09. Strong uniqueness for certain infinite dimensional Dirichlet operators and applications to stochastic quantization. https://arxiv.org/abs/math/9801144

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