Trotter’s approximation of semigroups and order of convergence in C2,αC2,α-spaces

We improve the quantitative estimate of the convergence in Trotter’s approximation theorem and obtain a representation of the resolvent operators in terms of iterates of linear operators on its whole domain. In the context of the standard simplex we give some estimates for functions of class C2,αC2,α which considerably improve some previous estimates and allow one to establish a partial inverse result.