The Nehari problem for the Pritchard-Salamon class of infinite- dimensional linear systems: A direct approach (Q1329560)

The authors give an elementary derivation for the solution of the Nehari- problem for the symbol \(G(s)= C(sI- A)^{-1} B\), where \(\Sigma(A,B,C)\) is a regular Pritchard-Salamon system with \(A\) the infinitesimal generator of an exponentially stable \(C_ 0\)-semigroup on the separable Hilbert spaces \(V\), \(W\) and \(Z\). This allows for the possibility that \(B\) and \(C\) be unbounded and have infinite rank. The approach exploits properties of regular Pritchard-Salamon systems and a new idea on \(J\)- spectral factorizations due to Green et al. The approach reduces the problem to the solution of an equivalent \(J\)-spectral factorization problem for this particular realization.