Wiener-Hopf operators with oscillating symbols and convolution operators on a union of intervals
type: Item
instance of: scholarly article
title: Wiener-Hopf operators with oscillating symbols and convolution operators on a union of intervals
zbMATH Open document ID: 0781.47033
DOI: 10.1007/BF01203121
published in: Integral Equations and Operator Theory
publication date: 1993-06-29T00:00:00Z
review text: Wiener-Hopf operators associated with matrix-valued symbols containing oscillating functions are studied from the point of view of Fredholm properties. The operators considered act between Sobolev spaces \(H_ \alpha(\mathbb{R})\) and are assumed to be of the general form \[ T_ w=r_ +F^{-1}WFI_ +:H^ +_ \alpha(\mathbb{R})\to H_ \beta(\mathbb{R}^ +), \] where \(H^ +_ \alpha(\mathbb{R})\) is the subspace of \(H_ \alpha(\mathbb{R})\) of elements with support contained in \(\mathbb{R}^ +\), \(H_ \beta(\mathbb{R}^ +)\) is the space of restrictions to \(\mathbb{R}^ +\) of distributions from \(H_ \beta(\mathbb{R})\), \(r_ +\) is the restriction operator to \(\mathbb{R}^ +\), \(I_ +\) is the extension operator to \(\mathbb{R}\), \(W\) is a matrix-valued function containing oscillating entries. The approach followed in this paper is based on a theorem of reduction of the symbol \(W(\xi)\) to a standard symbol \(G_ 0(\xi)\) i.e. a symbol possessing limits as \(\xi\to\pm\infty\) along the real line. The application to Fredholm properties of the convolution operators on a union of intervals is given.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 222050
zbMATH Keywords: Wiener-Hopf operators associated with matrix-valued symbols containing oscillating functions
zbMATH Keywords: Fredholm properties
zbMATH Keywords: Sobolev spaces
author: M. Amélia Bastos
author: António F. dos Santos
reviewed by: Vladimir Rabinovich
MaRDI profile type: Publication
cites work: Convolution equations of the first kind on a finite interval in Sobolev spaces
cites work: Q3907885
cites work: A note on first kind convolution equations on a finite interval
full work available at URL: https://doi.org/10.1007/bf01203121
OpenAlex ID: W1994576062
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description: scientific article; zbMATH DE number 222050