Singular integral operators in a weighted \(L^ 2\)-space
type: Item
instance of: scholarly article
title: Singular integral operators in a weighted \(L^ 2\)-space
zbMATH Open document ID: 0581.47037
DOI: 10.1007/BF01202905
author: Stephen T. Welstead
published in: Integral Equations and Operator Theory
publication date: 1985-01-01T00:00:00Z
review text: Cauchy singular integral operators are characterized as operators in a weighted \(L^ 2\)-space. The integral operator arises from a singular integral equation with variable coefficients. An appropriate weight function associated with the singular integral operator is constructed, and the set of polynomials orthogonal with respect to this weight function is defined. The action of the operator on polynomial sets is studied, and the definition of the operator is extended to a weighted \(L^ 2\)-space. In this space, the operator is shown to be bounded, and, in some cases, isometric. Formulas are developed for the composition of the singular integral operator and its one sided inverse.
Mathematics Subject Classification ID: 47Gxx
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 3929779
zbMATH Keywords: Cauchy singular integral operators
zbMATH Keywords: operators in a weighted \(L^ 2\)- space
zbMATH Keywords: weight function
MaRDI profile type: Publication
cites work: Q3278549
cites work: The Numerical Solution of Singular Integral Equations over $( - 1,1)$
cites work: Orthogonal Polynomials Associated with Singular Integral Equations Having a Cauchy Kernel
cites work: Q5681646
cites work: Q5820804
cites work: Q3966611
cites work: ON THE FINITE HILBERT TRANSFORMATION
cites work: Boundary conditions at infinity for difference equations of limit-circle type
description: scientific article; zbMATH DE number 3929779