Cascade Connections of Linear Systems and Factorizations of Holomorphic Operator Functions Around a Multiple Zero in Several Variables
| dc.creator | Kalyuzhniy, Dmitriy S. | |
| dc.date | 2000-02-04 | |
| dc.date.accessioned | 2026-07-07T04:33:35Z | |
| dc.date.available | 2026-07-07T04:33:35Z | |
| dc.description | We show that the factorization problem $θ(z)=θ_2(z)θ_1(z)$ is solvable in the class of Hilbert space operator-valued functions holomorphic on some neighbourhood of $z=0$ in $\nspace{C}{N}$ and having a zero at $z=0$ (here $θ(z)$ has a multiple zero at $z=0$). Such a factorization problem becomes more complicated if we demand for $θ(z), θ_1(z)$ and $θ_2(z)$ to be Agler--Schur-class functions on the polydisk $\nspace{D}{N}$ and for the factorization identity to hold in $\nspace{D}{N}$. In this case we reduce it to the problem on the existence of a cascade decomposition for certain multiparametric linear system $α$--a conservative realization of $θ(z)$, and give the criterion for its solvability in terms of common invariant subspaces for the $N$-tuple of main operators of $α$. | |
| dc.description | LaTeX, 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0002033 | |
| dc.identifier | http://arxiv.org/abs/math/0002033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58631 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47A56, 93B15, 93C35 | |
| dc.title | Cascade Connections of Linear Systems and Factorizations of Holomorphic Operator Functions Around a Multiple Zero in Several Variables | |
| dc.type | text |