On block completion problems for Arov-normalized \(j_{qq}-J_{q}\)-elementary factors
type: Item
instance of: scholarly article
title: On block completion problems for Arov-normalized \(j_{qq}-J_{q}\)-elementary factors
zbMATH Open document ID: 0999.47014
DOI: 10.1016/S0024-3795(01)00523-7
author: B. Fritzsche
author: B. Kirstein
author: Mirko Mosch
published in: Linear Algebra and its Applications
publication date: 2002-06-24T00:00:00Z
review text: It is well known that the matrix completion problems are equivalent to interpolation problems for classes of analytic functions. It was also understood very early in the development of this dictionary that considering indefinite metric spaces can simplify and illuminate classical computations first considered by Schur, Carathéodory and Nevanlinna and can be used in Hamiltonian mechanics problems. The present note is a part of an ample programme advocated by the first two authors. Specifically, the note deals with a non-degenerate Carathéodory interpolation problem, for matrix valued analytic functions, which are contractive (respectively unitary on the boundary) with respect to a \(J\)-inner product structure. The work is based on old ideas of Potapov and their more recent ramifications due to Arov. See for instance: \textit{D. Z. Arov} [Teor. Funkts. Funkts. Anal. Priloz. 51, 61-67 (1989; Zbl 0701.41006); ibid. 52, 103-109 (1989; Zbl 0737.41001); ibid. 53, 57-65 (1990; Zbl 0738.47015)].
reviewed by: Mihai Putinar
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 47A56
zbMATH DE Number: 1758618
zbMATH Keywords: matrix completion problems
zbMATH Keywords: interpolation problems
zbMATH Keywords: Hamiltonian mechanics
zbMATH Keywords: non-degenerate Carathéodory interpolation problem
zbMATH Keywords: matrix valued analytic functions
zbMATH Keywords: \(J\)-inner product
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1758618