A conservative de Branges-Rovnyak functional model for operator Schur functions on C+

D4 Published development or research report or study

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Publication Details

List of Authors: Joseph A. Ball, Mikael Kurula, Olof J. Staffans
Publisher: arXiv.org
Publication year: 2017


We present a solution of the operator-valued Schur-function realization
problem on the right-half plane by developing the corresponding de
Branges-Rovnyak canonical conservative simple functional model. This model
corresponds to the closely connected unitary model in the disk setting, but we
work the theory out directly in the right-half plane, which allows us to
exhibit structure which is absent in the disk case. A main feature of the study
is that the connecting operator is unbounded, and so we need to make use of the
theory of well-posed continuous-time systems. In order to strengthen the
classical uniqueness result (which states uniqueness up to unitary similarity),
we introduce non-invertible intertwinements of system nodes.

Last updated on 2020-07-04 at 06:11