Abstract
We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator matrices considered in (Trostorff in J Funct Anal 267(8):2787–2822, 2014), which can be characterized in terms of an associated boundary relation.
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Notes
For a closed linear operator C we denote by \({\mathcal {D}}_{C}\) its domain, equipped with the graph-norm of C.
We note that in [10] an additional operator \(G\in L(E_{0},E_{0}')\) is incorporated in A, which we will omit for simplicity.
Recall that the norm on \(E_{0}\) is equivalent to the graph norm of \(\left( \begin{array}{c} L\\ K \end{array}\right) \).
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Communicated by George Weiss.
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Trostorff, S. On a Class of Block Operator Matrices in System Theory. Complex Anal. Oper. Theory 11, 947–960 (2017). https://doi.org/10.1007/s11785-016-0556-1
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DOI: https://doi.org/10.1007/s11785-016-0556-1