Generalized factorization for Daniele-Khrapkov matrix functions -- explicit formulas
type: Item
instance of: scholarly article
title: Generalized factorization for Daniele-Khrapkov matrix functions -- explicit formulas
zbMATH Open document ID: 0824.45005
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-11-14T00:00:00Z
review text: The problem of calculating the factors of a canonical generalized factorization of a class of non-rational matrix-valued functions of Daniele-Khrapkov type is solved. The method followed in the paper is a modification of that used for the investigation of conditions for the existence of canonical factorizations proposed by the authors in [ibid. 190, No. 1, 142-164 (1995; reviewed above)]. It is shown that the solutions of the Riemann-Hilbert problem with coefficient \(G\) which give the factors of \(G\) are related by a simple recursive system of algebraic equations to the homogeneous Riemann-Hilbert problem corresponding to the calculation of the functions in the kernel of a Toeplitz operator whose symbol \(\widetilde G\) possesses a non-canonical factorization. As a by-product of the analysis the authors solve explicitly an old problem stated by Daniele, that of determining a rational function \(R\) in the same group as \(G\), such that the factors in the factorization of \(RG\) belong to this group. These factors are then given by simple formulas analogous to those for the case where \(\rho\) is the square-root of the quotient of first degree polynomials. An example related to applications in diffraction theory is given.
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 765127
zbMATH Keywords: Wiener-Hopf operator
zbMATH Keywords: canonical generalized factorization
zbMATH Keywords: non-rational matrix-valued functions of Daniele-Khrapkov type
zbMATH Keywords: Riemann-Hilbert problem
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.1995.1079
OpenAlex ID: W2011997564
DOI: 10.1006/JMAA.1995.1079
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description: scientific article; zbMATH DE number 765127