Cascade Connection of Multiparametric Linear Systems and a Conservative Realization of Decomposable Inner Operator Functions in Bidisk
Abstract
We introduce the notion of cascade connection of multiparametric discrete timeinvariant linear dynamical systems with unit delay. This allows us to construct the explicit example of conservative realization of a decomposable operatorvalued function $\theta (z_1, z_2)=\theta_2(z_2)\theta_1(z_1)$, where $\theta_1$ and $\theta_2$ are inner operatorvalued functions on the unit disk, vanishing at zero, and discuss some properties of such realization.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2000
 arXiv:
 arXiv:math/0002208
 Bibcode:
 2000math......2208K
 Keywords:

 Mathematics  Functional Analysis;
 47A56;
 93B15;
 93C35
 EPrint:
 In Russian (English abstract), PostScript, 16 pages