Chandrasekhar equations for infinite dimensional systems

In this paper we state results on the existence of Chandrasekhar equations for linear time invariant systems defined on Hilbert spaces. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a ´strong´ solution of the Riccati differential equation. A discussion of the linear quadratic optimal control problem for hereditary differential systems is also included.