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arXiv · 0712.3729

Passive systems with a normal main operator and quasi-selfadjoint systems

Yu. M. Arlinskiĭ·S. Hassi·H. S. V. de Snoo
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Abstract

Passive systems $\tau={T,M,N,H}$ with $M$ and $N$ as an input and output space and $H$ as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given and a general unitary similarity result involving some spectral theoretic conditions on the main operator is established. A passive system $\tau$ with $M=N$ is said to be quasi-selfadjoint if $ran(T-T^*)\subset N$. The subclass $S^{qs}$ of the Schur class $S$ is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass $S^{qs}$ is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function belonging to the subclass $S^{qs}$ and the $Q$-function of $T$ is given.

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Yu. M. Arlinskiĭ, S. Hassi, H. S. V. de Snoo. 2007-12-21. Passive systems with a normal main operator and quasi-selfadjoint systems. https://arxiv.org/abs/0712.3729

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