A Conservative de Branges-Rovnyak Functional Model for Operator Schur Functions on C+

作者：Ball Joseph A.; Kurula Mikael^*; Staffans Olof J.

来源：Complex Analysis and Operator Theory, 2018, 12(4): 877-915.

DOI：10.1007/s11785-017-0746-5

• Schur function
• Continuous time
• Linear system
• Right half-plane
• Functional model
• de Branges-Rovnyak
• Realization
• Reproducing kernel

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.

• 出版日期2018-4
• 单位美国弗吉尼亚理工大学(Virginia Tech)