Geodesic
Reproducing Kernels and Riccati Equations
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 1, pp. 35-53

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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: J-inner matrix valued functions, J-unitary matrix valued functions, Riccati equations, Lyapunov equations, reproducing kernel spaces, de Branges spaces
Mots-clés : równanie różniczkowe Riccatiego, jądro reprodukujące 
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     author = {Dym, H.},
     title = {Reproducing {Kernels} and {Riccati} {Equations}},
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Dym, H. Reproducing Kernels and Riccati Equations. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 1, pp. 35-53. http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_1_a1/