Composition of infinite-dimensional Dirac structures


Kurula, Mikael and Schaft, Arjan van der and Zwart, Hans (2006) Composition of infinite-dimensional Dirac structures. In: 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006, 24-28 July 2006, Kyoto, Japan (pp. pp. 27-32).

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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.
Item Type:Conference or Workshop Item
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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