Generalized factorization for a class of non-rational 2\(\times 2\) matrix functions
type: Item
instance of: scholarly article
title: Generalized factorization for a class of non-rational 2\(\times 2\) matrix functions
zbMATH Open document ID: 0712.15019
DOI: 10.1007/BF01732318
published in: Integral Equations and Operator Theory
publication date: 1990-01-01T00:00:00Z
review text: The authors study the generalized factorization for the class of \(2\times 2\) piecewise continuous matrix functions on \({\dot {\mathbb{R}}}={\mathbb{R}}\cup \{\infty \}\) which are of the form \[ G=\left[ \begin{matrix} 1\\ {\bar \rho}_ a'\end{matrix} \quad \begin{matrix} \lambda a\rho \\ 1\end{matrix} \right], \] where \(\rho\) is a complex-valued function such that \(\rho^ 2\) is a rational function of the form \[ \rho^ 2=(\frac{\omega -k)}{\omega +k_ 1})^ n,\quad k,k_ 1\in {\mathbb{C}}\setminus {\mathbb{R}},\quad n\quad natural, \] \(a\) is an arbitrary piecewise continuous function and \(\lambda\in {\mathbb{C}}\). A space transformation is used to reduce the problem to the generalized factorization of a scalar piecewise continuous function on a contour in the complex plane.
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 47A56
zbMATH DE Number: 4171125
zbMATH Keywords: Daniele-Khrapkov matrices
zbMATH Keywords: Wiener-Hopf factorization
zbMATH Keywords: generalized factorization
zbMATH Keywords: piecewise continuous matrix functions
author: A. B. Lebre
author: António F. dos Santos
reviewed by: Ali-Akbar Jafarian
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01732318
OpenAlex ID: W2061814596
description: scientific article; zbMATH DE number 4171125