Multiparametric Passive Linear Stationary Dynamical Scattering Systems: Discrete Case, II: Existence of Conservative Dilations

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Abstract
In the present paper we introduce the notion of dilation of a multiparametric linear stationary dynamical system (systems of this type, in particular passive, and conservative scattering ones were first introduced in func-an/9804130). We establish the criterion for existence of a conservative dilation of a multiparametric passive scattering system. This allows to distinguish the class of so-called $N$-passive systems preserving the most important properties of one-parametric passive scattering systems.

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