Abstract
In this paper we consider realization problems for operator-valued R-functions acting on a Hilbert space E (dim E < ∞) as linear-fractional transformations of the transfer operator-valued functions (characteristic functions) of linear stationary conservative dynamic systems (Brodskii-Livsic rigged operator colligations). We give complete proofs of both the direct and inverse realization theorems announced in [6], [7].
Dedicated to the memory of Professor Israel Glazman
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Belyi, S.V., Tsekanovskii, E.R. (1997). Realization Theorems for Operator-Valued R-Functions. In: Gohberg, I., Lyubich, Y. (eds) New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8910-0_5
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DOI: https://doi.org/10.1007/978-3-0348-8910-0_5
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