The Propeties And Applactions Of C-Semigroups

The main work of this thesis is devided into two parts:We give nesserary and sufficient conditions on the C-resolvent of A to guarantee that the C-semigroup be an ideal of integral operators.We consider first order symmetric, hyperbolic systems of differential operator with constant coefficients on L~p-space. We show such system can be governed by a C-semigroup which extends a classical result of Brenner and then apply it to Dirac equation. Hieber and Nicaise have considered Dirac equation by using integrated semigroups, our result improves their work in that we are able to deal with the critical index case.