A Kernel Representation of Dirac Structures for Infinite-dimensional Systems. (19th August 2014) - Damanik, David; Ruzhansky, Michael; Vougalter, Vitali; Wong, M.W.; Iftime, O.V.; Roman, M.; Sandovici, A.
<x content-type="archive" xml:space="preserve">Abstract</x> 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.