H 2-Functions and Infinite Dimensional Realization Theory

In this paper, the realization question for infinite dimensional linear systems is examined for both bounded and unbounded operators. In addition to obtaining realizability criteria covering the basic cases, we discuss the relation between canonical realizations of the same system.What one finds is that the set of transfer functions, which are realizable by triples (A,b,c) with A bounded is related in a close way to the space of the complex functions analytic and square integrable on the disk |s| <1 and that the set of transfer functionsn which are realizable by triples (A,b,c) with  A unbounded but generating a strongly continuous semigroup is related in a close way to functions analytic and square integrable on a half-plane.