Generalized factorization for Daniele-Khrapkov matrix functions -- partial indices
type: Item
instance of: scholarly article
title: Generalized factorization for Daniele-Khrapkov matrix functions -- partial indices
zbMATH Open document ID: 0824.45004
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-11-14T00:00:00Z
review text: The authors deal with the problem of calculating the partial indices of generalized factorizations of non-rational matrix-valued functions \(G: \mathbb{R}\to \mathbb{C}^{2\times 2}\) of the form \(G= \left[\begin{smallmatrix} a &b\\ \rho^ 2 b &a\end{smallmatrix}\right]\), where \(a, b\in C(\dot\mathbb{R})\) and \(\rho\in C(\dot\mathbb{R})\) is the square-root of the quotient of two second degree polynomials such that \(a\pm \rho b\) possess bounded generalized factorizations (i.e., such that the factors and their inverses are bounded in their half-planes of analyticity). The partial indices give detailed information on the structure of the kernel and image of the associated Wiener-Hopf or Toeplitz operator in the non-canonical cases. In particular, necessary and sufficient conditions for the existence of canonical generalized factorizations are obtained.
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 47A68
zbMATH DE Number: 765115
zbMATH Keywords: Wiener-Hopf operators
zbMATH Keywords: Cauchy type singular integral equations
zbMATH Keywords: partial indices
zbMATH Keywords: generalized factorizations
zbMATH Keywords: non-rational matrix-valued functions
zbMATH Keywords: Toeplitz operator
author: M. C. Câmara
author: António F. dos Santos
author: M. Amélia Bastos
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1068
OpenAlex ID: W1996700540
DOI: 10.1006/JMAA.1995.1068
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description: scientific article; zbMATH DE number 765115