| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 5, 2014
Spectral problems
|
|
|---|---|---|
| Page(s) | 295 - 308 | |
| DOI | https://doi.org/10.1051/mmnp/20149520 | |
| Published online | 19 August 2014 | |
A Kernel Representation of Dirac Structures for Infinite-dimensional Systems
1 Department of Economics, Econometrics
and Finance, University of Groningen Nettelbosje 2, 9747 AE, Groningen, The Netherlands
2 Department of Mathematics, “Gheorghe
Asachi” Technical University B-dul Carol I, nr. 11, 700506, Iaşi, Romania
⋆
Corresponding author. E-mail: adrian.sandovici@luminis.ro
Dirac structures are used as the underlying structure to mathematically formalize port-Hamiltonian systems. This note approaches the Dirac structures for infinite-dimensional systems using the theory of linear relations on Hilbert spaces. First, a kernel representation for a Dirac structure is proposed. The one-to-one correspondence between Dirac structures and unitary operators is revisited. Further, the proposed kernel representation and a scattering representation are constructively related. Several illustrative examples are also presented in the paper.
Mathematics Subject Classification: 93A30 / 93B28
Key words: Dirac structure / linear relation / Hilbert space / infinite–dimensional system
© EDP Sciences, 2014
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