Multiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete Case

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dc.creatorKalyuzhniy, Dmitriy S.
dc.date1998-04-28
dc.date1999-03-24
dc.date.accessioned2026-07-07T05:24:38Z
dc.date.available2026-07-07T05:24:38Z
dc.descriptionWe propose the new generalization of linear stationary dynamical systems with discrete time $t\in\mathbb{Z}$ to the case $t\in\nspace{Z}{N}$. The dynamics of such a system can be reproduced by means of its associated multiparametric Lax-Phillips semigroup. We define multiparametric passive, and conservative scattering systems and interpret them in terms of operator colligations, of the associated semigroup and of "energetic" relations for system data. We prove the Agler's type theorem describing the class of holomorphic operator-valued functions on the polydisc $\nspace{D}{N}$ that are the transfer functions of multiparametric conservative scattering systems. Keywords: Passive systems, multiparametric Lax-Phillips semigroup, generalized Schur class, conservative realizations
dc.descriptionLaTeX2e, 37 pages, no figures, Odessa State Academy of Civil Engineering, many improvements. accepted for publication
dc.identifierhttps://arxiv.org/abs/math/9804130
dc.identifierhttp://arxiv.org/abs/math/9804130
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76872
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subjectSpectral Theory
dc.subject93C35; 93B15; 32A10; 47A48
dc.titleMultiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete Case
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