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Multiparametric dissipative 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 dissipative, and conservative scattering ones were first introduced in [6]). We establish the criterion for existence of a conservative dilation of a multiparametric dissipative scattering system. This allows to distinguish the class of so-calledN-dissipative systems preserving the most important properties of one-parametric dissipative scattering systems.

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Authors and Affiliations

  1. Department of Higher Mathematics, Odessa State Academy of Civil Engineering and Architecture, Didrihson str. 4, 270029, Odessa, Ukraine

    Dmitriy S. Kalyuzhniy

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  1. Dmitriy S. Kalyuzhniy
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Research supported in part by the Ukrainian-Israeli project of scientific co-operation (contract no. 2M/1516-97).

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Kalyuzhniy, D.S. Multiparametric dissipative linear stationary dynamical scattering systems: Discrete case, II: Existence of conservative dilations. Integr equ oper theory 36, 107–120 (2000). https://doi.org/10.1007/BF01236289

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  • DOI: https://doi.org/10.1007/BF01236289

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