Admissibility of unbounded control operators

For linear systems described by dx(t)/dt = Ax(t) + Bu(t), where A generates a semigroup on the state space X and B is an unbounded operator, some necessary as well as sufficient conditions are given for B to be admissible, i.e., for any t, the state x(t) should be in X and should depend continuously on the input u member of L^p. This approach begins with an axiomatic description of such a system in terms of a functional equation. The results are applied to the wave equation on a bounded interval.