SUBORDINATION IN THE SENSE OF BOCHNER AND A RELATED FUNCTIONAL-CALCULUS

We prove a new representation of the generator of a subordinate semigr oup as limit of bounded operators. Our construction yields, in particu lar, a characterization of the domain of the generator. The generator of a subordinate semigroup can be viewed as a function of the generato r of the original semigroup. For a large class these functions we show that operations at the level of functions has its counterpart at the level of operators.