Essential self-adjointness of Dirichlet operators of Gibbs measures on infinite products of manifolds

We obtain the conditions of essential self-adjointness of Dirichlet operators of Gibbs measures with essential domains consisting of smooth cylindrical functions. It is proved that certain spaces of smooth functions are invariant under the action of the semigroup of the Dirichlet operator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 4–11, January, 1995.This research was partially supported by the Ukrainian State Committee on Science and Technology.