Locally Lipschitz continuous integrated semigroups

This paper is concerned with the problem of real characterization of locally Lipschitz continuous (n+1)-times integrated semigroups, where n is a nonnegative integer. It is shown that a linear operator is the generator of such an integrated semigroup if and only if it is closed, its resolvent set contains all sufficiently large real numbers, and a stability condition in the spirit of the finite difference approximation theory is satisfied.