Abstract
The notion of minimal realization of a pair of finite rank operators between Hilbert spaces is introduced. Constructions of such minimal realizations are made. A minimal realization of an integral operator with semi-separable kernel is constructed for the case that one of the realizations has analytic coefficients. A consequence for the characterization of minimal stability of an analytic minimal system is given.
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Peeters, G. On minimalization of time varying linear systems with well-posed boundary conditions. Integr equ oper theory 12, 42–66 (1989). https://doi.org/10.1007/BF01199756
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DOI: https://doi.org/10.1007/BF01199756