Multiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete Case

Dmitriy S. Kalyuzhniy

Multiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete Case

泛函分析 2007-05-23 v2 算子代数谱理论

作者: Dmitriy S. Kalyuzhniy

摘要

We 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

关键词

dynamical systems and chaos delay differential equations data-driven dynamical systems

引用

@article{arxiv.math/9804130,
  title  = {Multiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete Case},
  author = {Dmitriy S. Kalyuzhniy},
  journal= {arXiv preprint arXiv:math/9804130},
  year   = {2007}
}

备注

LaTeX2e, 37 pages, no figures, Odessa State Academy of Civil Engineering, many improvements. accepted for publication

Multiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete Case

摘要

关键词

引用

备注

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