Composition of infinite-dimensional Dirac structures

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

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    Abstract

    In this paper, we define the Dirac structure and give some fundamental tools for its study.We then proceed by defining composition of ``split Dirac structures''. In the finite-dimensional case, composition of two Dirac structures always result in a new Dirac structure, but in the Hilbert space setting this result no longer holds. Thus, the problem of finding necessary and sufficient conditions for the composition of two infinite-dimensional Dirac structures to itself be a Dirac structure arises very naturally. The main result of this paper provides these necessary and sufficient conditions. In addition, we give examples and relate conposition of Dirac structures to the Redheffer star product of unitary operators.
    Original languageUndefined
    Title of host publicationProceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems
    EditorsY Yamamoto
    Place of PublicationKyoto
    PublisherErasmus University Rotterdam
    Pages27-32
    Number of pages6
    ISBN (Print)not assigned
    Publication statusPublished - 28 Jul 2006
    Event17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 - Kyoto, Japan
    Duration: 24 Jul 200628 Jul 2006
    Conference number: 17

    Publication series

    Name
    Numbersupplement

    Conference

    Conference17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006
    Abbreviated titleMTNS
    CountryJapan
    CityKyoto
    Period24/07/0628/07/06

    Keywords

    • MSC-93C25
    • MSC-46C20
    • IR-66606
    • METIS-237614
    • EWI-8148

    Cite this

    Kurula, M., van der Schaft, A., & Zwart, H. J. (2006). Composition of infinite-dimensional Dirac structures. In Y. Yamamoto (Ed.), Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (pp. 27-32). Kyoto: Erasmus University Rotterdam.