The applications of C-semigroups to the Dirac equation

In this paper, we study first-order symmetric, hyperbolic systems of differential operator with constant coefficients on L p -spaces. We show that such systems can be governed by some C -semigroups and as an application we consider the Dirac equation. Our result improves that of Nicaise [S. Nicaise, The Hille–Yosida and Trotter–Kato theorems for integrated semigroups, J. Math. Anal. Appl. 180 (1993) 303–316].