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

Joseph A. Ball, Mikael Kurula, Olof J. Staffans

Research output: Book/ReportCommissioned reportProfessional

Abstract

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

Original languageUndefined/Unknown
PublisherarXiv.org
Publication statusPublished - 2017
MoE publication typeD4 Published development or research report or study

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