ON THE INVERSION OF THE LAPLACE TRANSFORM OF C-O SEMIGROUPS AND ITS APPLICATIONS

The main results are as follows: (a) The inversion of the Laplace tran sform of C-0 semigroup representation in a Hilbert space H is generali zed to all x is an element of H. (b) A full characterization is given in terms of the resolvent R(lambda; A) of the infinitesimal generator A of a C-0 semigroup T(t) in a Hilbert space, which assures the contin uity of T(t) for t > 0 in the uniform operator topology.