Singular integral operators with coefficients of a special structure related to operator equalities
type: Item
instance of: scholarly article
title: Singular integral operators with coefficients of a special structure related to operator equalities
zbMATH Open document ID: 1194.47055
author: Aleksandr Karelin
published in: Complex Analysis and Operator Theory
publication date: 2009-12-14T00:00:00Z
review text: The Cauchy singular integral operator along a contour \(\Gamma\) \[ (S_{\Gamma}\varphi)(t)=\frac{1}{\pi i}\int\limits_{\Gamma}\frac{\varphi(\tau)}{\tau-t} \,d\tau \] is considered and operator equalities are used for the study of matrix characteristic singular integral operators. The Gohberg-Krupnik matrix equality is used for the study of questions connected with the invertibility problem. The author also considers a singular integral operator with orientation preserving shift on the unit circle and coefficients generated by piecewise constant functions, functions \(t\) and \(t^{-1}\), and possessing special properties. Using the operator equality, conditions for invertibility of this operator are obtained. Conditions for the invertibility of matrix characteristic singular integral operators with four-valued piecewise constant coefficients of a special structure are likewise obtained.
reviewed by: Alexander N. Tynda
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45P99
zbMATH DE Number: 5646600
zbMATH Keywords: Cauchy kernel
zbMATH Keywords: singular integral operator
zbMATH Keywords: matrix characteristic operator
zbMATH Keywords: piecewise constant coefficients
zbMATH Keywords: invertibility
MaRDI profile type: Publication
full work available at URL: s11785-008-0066-x
OpenAlex ID: W2150795746
DOI: 10.1007/S11785-008-0066-X
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description: scientific article; zbMATH DE number 5646600