Lototsky-Schnabl operators associated with a strictly elliptic differential operator and their corresponding feller semigroup

Given an open bounded convex subset Omega of R-p, a strictly elliptic diffe rential operator L and a continuous function lambda : <(Omega)over bar> --> [0, 1], and denoted with T-L the Dirichlet operator associated with L, the Lototsky-Schnabl operators associated with T-L and lambda are investigated . In particular, conditions are established which ensure the existence of a Feller semigroup represented by Limit of powers of these operators. Then t he analytic expression of the infinitesimal generator is determined and som e properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined.