Passive Systems with a Normal Main Operator and Quasi-selfadjoint Systems

Yury M. Arlinskii, Seppo Hassi*, Henk S. V. de Snoo

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)

    Abstract

    Passive systems t = {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 t with M = N is said to be quasi-selfadjoint if ran (T - T*). N. The subclass S(qs)(N) of the Schur class S(N) is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass S(qs)(N) is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function belonging to the subclass S(qs) (N) and the Q-function of T is given.

    Original languageEnglish
    Pages (from-to)19-56
    Number of pages38
    JournalComplex analysis and operator theory
    Volume3
    Issue number1
    DOIs
    Publication statusPublished - Mar-2009

    Keywords

    • Passive system
    • transfer function
    • quasi-selfadjoint contraction
    • Q-function
    • DISCRETE-TIME-SYSTEMS
    • HERMITIAN CONTRACTIONS
    • SCATTERING SYSTEMS
    • EXTENSIONS
    • MATRICES
    • KREIN

    Fingerprint

    Dive into the research topics of 'Passive Systems with a Normal Main Operator and Quasi-selfadjoint Systems'. Together they form a unique fingerprint.

    Cite this