Dirac structures and their composition on Hilbert spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:372

Article

Kurula, Mikael¹  Zwart, Hans²  van der Schaft, Arjan³  Behrndt, Jussi⁴ 

[1] Abo Akad Univ, Dept Math, FIN-20500 Turku, Finland

[2] Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands

[3] Univ Groningen, Dept Math & Comp Sci, NL-9700 AV Groningen, Netherlands

[4] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

关键词: Dirac structure;    Composition;    Boundary triplet;    Boundary colligation;    Impedance conservative;    Krein space;   

DOI  :  10.1016/j.jmaa.2010.07.004

来源: Elsevier

【 摘 要 】

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 Krein 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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free