### Abstract

Original language | Undefined |
---|---|

Title of host publication | Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems |

Editors | Y Yamamoto |

Place of Publication | Kyoto |

Publisher | Erasmus University Rotterdam |

Pages | 27-32 |

Number of pages | 6 |

ISBN (Print) | not assigned |

Publication status | Published - 28 Jul 2006 |

Event | 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 - Kyoto, Japan Duration: 24 Jul 2006 → 28 Jul 2006 Conference number: 17 |

### Publication series

Name | |
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Number | supplement |

### Conference

Conference | 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 |
---|---|

Abbreviated title | MTNS |

Country | Japan |

City | Kyoto |

Period | 24/07/06 → 28/07/06 |

### Keywords

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

### Cite this

*Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems*(pp. 27-32). Kyoto: Erasmus University Rotterdam.

}

*Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems.*Erasmus University Rotterdam, Kyoto, pp. 27-32, 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006, Kyoto, Japan, 24/07/06.

**Composition of infinite-dimensional Dirac structures.** / Kurula, Mikael; van der Schaft, Arjan; Zwart, Heiko J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Composition of infinite-dimensional Dirac structures

AU - Kurula, Mikael

AU - van der Schaft, Arjan

AU - Zwart, Heiko J.

PY - 2006/7/28

Y1 - 2006/7/28

N2 - 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.

AB - 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.

KW - MSC-93C25

KW - MSC-46C20

KW - IR-66606

KW - METIS-237614

KW - EWI-8148

M3 - Conference contribution

SN - not assigned

SP - 27

EP - 32

BT - Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems

A2 - Yamamoto, Y

PB - Erasmus University Rotterdam

CY - Kyoto

ER -