Dirichlet operators semigroups in some Gibbs lattice spin systems. (English) Zbl 0873.47027

Albeverio, S.; Antoniouk, A. Val.; Antoniouk, A. Vict.; Kondratiev, Yu. G.

Methods Funct. Anal. Topol. 1, No. 1, 3-27 (1995).

Summary: We investigate the Dirichlet operators semigroups associated with Gibbs measures on infinite products of compact Riemannian manifolds. We show the invariance of special Banach spaces of smooth functions under the action of these semigroups. As a consequence, we obtain the essential selfadjointness of generators which corresponds to the uniqueness of stochastic dynamics.

MSC:

47D07	Markov semigroups and applications to diffusion processes
60H15	Stochastic partial differential equations (aspects of stochastic analysis)
47B25	Linear symmetric and selfadjoint operators (unbounded)
60J45	Probabilistic potential theory
47D06	One-parameter semigroups and linear evolution equations

Keywords:

Dirichlet operators semigroups; Gibbs measures; infinite products of compact Riemannian manifolds; invariance; essential selfadjointness of generators; uniqueness of stochastic dynamics