Wiener-Hopf factorization, inverse Fourier transforms and exponentially dichotomous operators
type: Item
instance of: scholarly article
title: Wiener-Hopf factorization, inverse Fourier transforms and exponentially dichotomous operators
zbMATH Open document ID: 0606.47021
DOI: 10.1016/0022-1236(86)90055-8
author: I. Gohberg
author: Harm Bart
author: Marinus Kaashoek
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: For a certain class of matrix functions that are analytic on the real line but not at infinity an explicit method of factorization and of constructing inverse Fourier transforms is developed. This method is applied to invert Wiener-Hopf integral equations on the half line and the full line. The results obtained extend analogous results of the authors for rational matrix functions and for functions that are analytic on the real line and at infinity. The analysis is based on an infinite dimensional realization theorem which involves operators that are a direct sum of two infinitesimal generators of \(C_ 0\)-semigroups of negative exponential type, one of which has support on the negative half line and the other on the positive half line. The latter operators are called exponentially dichotomous and the study of their properties forms an essential part of the paper.
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 3979822
zbMATH Keywords: matrix functions
zbMATH Keywords: factorization
zbMATH Keywords: inverse Fourier transforms
zbMATH Keywords: Wiener-Hopf integral equations
zbMATH Keywords: infinite dimensional realization theorem
zbMATH Keywords: \(C_ 0\)- semigroups of negative exponential type
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90055-8
OpenAlex ID: W2036400803
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description: scientific article; zbMATH DE number 3979822