Kurula, Mikael (Abo Akademi Univ.), van der Schaft, Arjan (Univ. of Groningen), Zwart, Hans (Univ. of Twente)

Composition of Infinite-Dimensional Linear Dirac-Type Structures

Scheduled for presentation during the Regular Session "Infinite Dimensional and Distributed Parameter Systems I" (MoA06), Monday, July 24, 2006, 10:50−11:15, Room G

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

In our 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 results 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 our paper provides these necessary and sufficient conditions. In addition, we give examples and relate composition of Dirac structures to the Redheffer star product of unitary operators.