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), whereA is a uniformly strongly elliptic operator of order two with smooth coefficients defined on a bounded open domain ofR _d ,B=AB _D andB _D is the Dirichlet map associated with Dirichlet boundary conditions andC is a bounded observation map fromL ₂() to the output spaceY. The approach is to solve an equivalentJ-spectral factorization problem for this particular realization.