The Nehari problem for infinite-dimensional linear systems of parabolic type

A complete solution is obtained to the suboptimal Nehari extension problem for transfer functions of parabolic systems with Dirichlet boundary control and smooth observations. The solutions are given in terms of the realization (-A, B, C), where A is a uniformly strongly elliptic operator of order two with smooth coefficients defined on a bounded open domain Omega of R(d), AB(D) and B-D is the Dirichlet map associated with Dirichlet boundary conditions and C is a bounded observation map from L(2)(Omega) to the output space Y. The approach is to solve an equivalent J-spectral factorization problem for this particular realization.