Journal of the Korean Mathematical Society (대한수학회지)
- Volume 32 Issue 3
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- Pages.447-459
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- 1995
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
The state space of a canonical linear system
Abstract
A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].