Reproducing kernels and Riccati equations - Dym, Harry (Zielona Góra: Uniwersytet Zielonogórski)
The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix valued functions that are J-unitary on the imaginary axis in a natural way.
Keywords: Riccati equations; Lyapunov equations; reproducing kernel spaces; de Branges spaces; J-inner matrix valued functions; J-unitary matrix valued functions