Factorization of piecewise valued matrix functions and its applications
type: Item
instance of: scholarly article
title: Factorization of piecewise valued matrix functions and its applications
zbMATH Open document ID: 0631.45005
DOI: 10.1016/0022-247X(87)90229-0
author: B. A. Kon
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: Let \(\Gamma\equiv \cup^{s-1}_{j=0}\Gamma_ j\) be the positively oriented boundary of an s-connected compact domain \(D^+_{\Gamma}\), \(\Gamma_ j\) (0\(\leq j\leq s-1)\) be closed Lyapunov contours with \(\Gamma_ j\cap \Gamma_ k=\emptyset\) (j\(\neq k)\), and assume that \(\Gamma_ 0\) contains the contours \(\Gamma_ j\) \((j=1,2,...,s-1)\) in its interior. Let T(z) be an \(n\times n\) piecewise matrix valued function defined on each of components \(\Gamma_ j\) of \(\Gamma\) as follows: For \(z\in \Gamma_ j\), \(j=0,1,...,s-1\), (1) \(T(z)=T_ j(z)\), where \(T_ j(z)\) is a holomorphic matrix function in some neighborhood of \(\Gamma_ j.\) The main purpose of this paper is to present explicit expressions for the factors and partial indices of factorization of some classes of piecewise matrix functions given by (1). These formulas are given in terms of common zeros in \(D^+_{\Gamma}\) of some polynomials associated with the matrix functions \(T_ j(z)\).
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 4026077
zbMATH Keywords: Wiener-Hopf equation
zbMATH Keywords: partial index
zbMATH Keywords: piecewise matrix function
zbMATH Keywords: factorization
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4026077