2011/09/19 by Yury Arlinskii̇̆, Arlinskii, Yury
Computer Science · Mathematics · #47A48 #47A56 #47A57 #47A64 #47B35 #47N70 #93B05 #93B07 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1109.4020
openalex publication_date 2011/09/19 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
We establish connections between Schur parameters of the Schur class operator-valued functions, the corresponding simple conservative realizations, lower triangular Toeplitz matrices, and Kre\uın shorted operators. By means of Schur parameters or shorted operators for defect operators of Toeplitz matrices necessary and sufficient conditions for a simple conservative discrete-time system to be controllable/observable and for a completely non-unitary contraction to be completely non-isometric/completely non-co-isometric are obtained. For the Schur problem a characterization of central solution and uniqueness criteria to the solution are given in terms of shorted operators for defect operators of contractive Toeplitz matrices, corresponding to data.