Composition of infinite-dimensional Dirac structures

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

Composition of infinite-dimensional Dirac structures

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

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

113 Downloads (Pure)

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 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
Number	supplement

Conference

Conference	17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006
Abbreviated title	MTNS
Country/Territory	Japan
City	Kyoto
Period	24/07/06 → 28/07/06

Keywords

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

Access to Document

http://www-ics.acs.i.kyoto-u.ac.jp/~mtns2006/MTNS2006.pdf

Cite this

@inproceedings{ae74ab055e8e4db88f6608a72be6066a,

title = "Composition of infinite-dimensional Dirac structures",

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.",

keywords = "MSC-93C25, MSC-46C20, IR-66606, METIS-237614, EWI-8148",

author = "Mikael Kurula and {van der Schaft}, Arjan and Zwart, {Heiko J.}",

year = "2006",

month = jul,

day = "28",

language = "Undefined",

isbn = "not assigned",

publisher = "Erasmus University Rotterdam",

number = "supplement",

pages = "27--32",

editor = "Y Yamamoto",

booktitle = "Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems",

address = "Netherlands",

note = "17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 ; Conference date: 24-07-2006 Through 28-07-2006",

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Kurula, M, van der Schaft, A & Zwart, HJ 2006, Composition of infinite-dimensional Dirac structures. in Y Yamamoto (ed.), 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. <http://www-ics.acs.i.kyoto-u.ac.jp/~mtns2006/MTNS2006.pdf>

Composition of infinite-dimensional Dirac structures. / Kurula, Mikael; van der Schaft, Arjan; Zwart, Heiko J.
Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. ed. / Y Yamamoto. Kyoto: Erasmus University Rotterdam, 2006. p. 27-32.

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.

N1 - Conference code: 17

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

T2 - 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006

Y2 - 24 July 2006 through 28 July 2006

ER -