\(J_{\ell}\)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting
type: Item
instance of: scholarly article
title: \(J_{\ell}\)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting
zbMATH Open document ID: 1113.47009
author: Daniel Alpay
author: A. Dijksma
author: Heinz Langer
published in: Linear Algebra and its Applications
publication date: 2007-02-14T00:00:00Z
review text: In this important paper, the authors introduce for the first time a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational \(J\)-unitary matrix functions into elementary factors from the same class.
reviewed by: Paşc Găvruţă
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 47A68
zbMATH DE Number: 5126038
zbMATH Keywords: Schur transformation
zbMATH Keywords: generalised Nevanlinna functions
zbMATH Keywords: kernel with negative squares
zbMATH Keywords: J-unitarity
zbMATH Keywords: minimal factorizations
zbMATH Keywords: reproducing kernel Pontryagin spaces
zbMATH Keywords: elementary rational matrix functions
MaRDI profile type: Publication
full work available at URL: j.laa.2006.06.010
OpenAlex ID: W2170779380
cites work: Q3838498
cites work: Q4534545
cites work: The Schur algorithm for generalized Schur functions. II: Jordan chains and transformations of characteristic functions
cites work: The Schur algorithm for generalized Schur functions. III: \(J\)-unitary matrix polynomials on the circle.
cites work: Q3436944
cites work: Q3973560
cites work: Factorization of \(J\)-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions
cites work: Schur functions, operator colligations, and reproducing kernel Pontryagin spaces
cites work: Q3724961
cites work: Structured invariant spaces of vector valued rational functions, Hermitian matrices, and a generalization of the Iohvidov laws
cites work: Topics in interpolation theory of rational matrix-valued functions
cites work: Q4038523
cites work: Fonctions méromorphes dans le cercle-unité et leurs séries de Taylor
cites work: Q3746076
cites work: Q4402889
cites work: Q3743572
DOI: 10.1016/J.LAA.2006.06.010
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description: scientific article; zbMATH DE number 5126038