On the Geometry of the Hermite – Fejér Interpolation Problem through Conservative Realizations
نویسندگان
چکیده
In this paper, we give state space realizations for the classical recursive solutions of operator-valued Carathéodory, Nevanlinna – Pick and Hermite – Fejér interpolation problems. These realizations are special in the sense that they satisfy an energy balance law; hence they are called conservative. Observability, controllability and minimality (including the property known as “simplicity”) of such realizations are studied, too. Finally, the main result of this paper is given, namely a geometric characterization for the McMillan degree of interpolants. This is a corrected version of the Mittag–Leffler preprint 2003/21; last edited on 8.4.2005. This work was supported in part by grants from the European Commission through the Program Training and Mobility of Researchers (TMR), the Swedish Research Council (VR) and the Mittag-Leffler Institute.
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