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A Kernel Representation of Dirac Structures forInfinite-dimensional Systems

Published online by Cambridge University Press:  19 August 2014

O.V. Iftime,
M. Roman and
A. Sandovici
O.V. Iftime
Affiliation:
Department of Economics, Econometrics and Finance, University of Groningen Nettelbosje 2, 9747 AE, Groningen, The Netherlands
M. Roman
Affiliation:
Department of Mathematics, “Gheorghe Asachi” Technical University B-dul Carol I, nr. 11, 700506, Iaşi, Romania
A. Sandovici*
Affiliation:
Department of Mathematics, “Gheorghe Asachi” Technical University B-dul Carol I, nr. 11, 700506, Iaşi, Romania
*
⋆Corresponding author. E-mail: adrian.sandovici@luminis.ro

Abstract

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Dirac structures are used as the underlying structure to mathematically formalizeport-Hamiltonian systems. This note approaches the Dirac structures forinfinite-dimensional systems using the theory of linear relations on Hilbert spaces.First, a kernel representation for a Dirac structure is proposed. The one-to-onecorrespondence between Dirac structures and unitary operators is revisited. Further, theproposed kernel representation and a scattering representation are constructively related.Several illustrative examples are also presented in the paper.

Keywords

Dirac structurelinear relationHilbert spaceinfinite–dimensional system

Information

Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 5: Spectral problems , 2014, pp. 295 - 308
Copyright
© EDP Sciences, 2014

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