Factorization of singular integral operators with a Carleman backward shift: the case of bounded measurable coefficients
type: Item
instance of: scholarly article
title: Factorization of singular integral operators with a Carleman backward shift: the case of bounded measurable coefficients
zbMATH Open document ID: 1190.47054
author: V. G. Kravchenko
author: A. B. Lebre
author: Juan Sebastián Rodríguez
published in: Journal d'Analyse Mathématique
publication date: 2009-12-14T00:00:00Z
review text: Using the factorization of matrix functions, the authors generalize some of their recently obtained results concerning scalar singular integral operators [J.~Integral Equations Appl.\ 13, No.\,4, 339--383 (2001; Zbl 1009.47034), Oper.\ Theory, Adv.\ Appl.\ 142, 189--211 (2003; Zbl 1057.47055), Math.\ Nachr.\ 280, No.\,9--10, 1157--1175 (2007; Zbl 1130.47028), in order to obtain an operator factorization. In the first two sections, necessary preliminaries are introduced, especially, important properties of the factors of the matrix factorization. The definition of a special matrix factorization is introduced in the third section of the paper, generalizing a previous result, and in the fourth section, a first step towards operator factorization is made. Studying representatives of anti-diagonal matrix functions, the fifth section concludes the operator factorization. Using the results from the previous section, in the sixth section the Fredholm properties of a singular integral operator with a backward shift are characterized, and in the last section, some examples and applications are made which allow a characterization for the set of invertible operators in that class. Also, some applications of the results to the class of generalized Toeplitz plus Hankel operators are presented.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 5646610
zbMATH Keywords: singular integral operators
zbMATH Keywords: Carleman backward shift
zbMATH Keywords: operator factorization
zbMATH Keywords: Toeplitz and Hankel operators
MaRDI profile type: Publication
full work available at URL: s11854-009-0001-8
OpenAlex ID: W2076190685
cites work: Factorization of matrix functions and singular integral operators
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cites work: Invertibility theory for Toeplitz plus Hankel operators and singular integral operators with flip.
cites work: Spectrum problems for singular integral operators with Carleman shift
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cites work: Factorization of singular integral operators with a Carleman shift via factorization of matrix functions: the anticommutative case
cites work: Banach algebras with symbol and singular integral operators. Transl. from the Russian by A. Iacob
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cites work: Composition operators and classical function theory
DOI: 10.1007/S11854-009-0001-8
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description: scientific article; zbMATH DE number 5646610