Pointwise estimates for the ground states of some classes of positivity preserving operators

We establish pointwise estimates for the ground states of some classes of posi- tivity preserving operators. The considered operators are negatively perturbed (by measures) strongly local Dirichlet operators. These estimates will be written in terms of the Green's kernel of the considered operators, whose existence will be proved. In many circumstances our estimates are even sharp so that they recover known results about the subject. The results will deserve to obtain large time heat kernel estimates for the related operators.