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Mathematical Modelling of Natural Phenomena Mathematical Modelling of Natural Phenomena

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A Kernel Representation of Dirac Structures for Infinite-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
E-mail address:
adrian.sandovici@luminis.ro
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Abstract

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.

Keywords

Dirac structure linear relation Hilbert space infinite–dimensional system
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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