Dirac structures and their composition on Hilbert spaces

Mikael Kurula, Heiko J. Zwart, Arjan van der Schaft, Jussi Behrndt

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    21 Citations (Scopus)
    75 Downloads (Pure)

    Abstract

    Dirac structures appear naturally in the study of certain classes of physical models described by partial differential equations and they can be regarded as the underlying power conserving structures. We study these structures and their properties from an operator-theoretic point of view. In particular, we find necessary and sufficient conditions for the composition of two Dirac structures to be a Dirac structure and we show that they can be seen as Lagrangian (hyper-maximal neutral) subspaces of Kreın spaces. Moreover, special emphasis is laid on Dirac structures associated with operator colligations. It turns out that this class of Dirac structures is linked to boundary triplets and that this class is closed under composition.
    Original languageEnglish
    Pages (from-to)402-422
    Number of pages21
    JournalJournal of mathematical analysis and applications
    Volume372
    Issue number2
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Composition
    • Impedance conservative
    • Boundary colligation
    • Krein space
    • Boundary triplet
    • Dirac structure

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