Abstract
We prove that an arbitrary function, which is holomorphic on some neighbourhood ofz=0 in ℂN and vanishes atz=0, and whose values are bounded linear operators mapping one separable Hilbert space into another one, can be represented as the transfer function of some multi-parameter discrete time-invariant conservative scattering linear system whose state space is a Krein space.
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The author is thankful to Prof. D.Z. Arov for suggesting this problem. He wishes also to thank Leeds University, where the revised version of this paper was prepared, for its hospitality, and Dr. V.V. Kisil who organized his visit there under the International Short Visits Scheme of LMS (grant no. 5620).
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Kalyuzhniy-Verbovetzky, D.S. OnJ-conservative scattering system realizations in several variables. Integr equ oper theory 43, 450–465 (2002). https://doi.org/10.1007/BF01212704
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DOI: https://doi.org/10.1007/BF01212704