Explicit formulae for J-spectral factors for regular linear systems

The standard way to obtain explicit formulas for spectral factorization problems for rational transfer functions is to use a minimal realization and then obtain formulae in terms of the generators A, B, C and D. For well-posed linear systems with unbounded generators these formulae will not always be well-defined. Instead, we suggest another approach for the class of well-posed linear systems for which zero is in the resolvent set of A. Such a system is related to a reciprocal system having bounded generating operators depending on B, C, D and the inverse of A. There are nice connections between well-posed linear systems and their reciprocal systems which allow us to translate a factorization problem for the well-posed linear system into one for its reciprocal system, the latter having bounded generating operators. We illustrate this general approach by giving explicit solutions to the sub-optimal Nehari problem.