On the solvability of singular integral equations with reflection on the unit circle
type: Item
instance of: scholarly article
title: On the solvability of singular integral equations with reflection on the unit circle
zbMATH Open document ID: 1220.45002
author: L. P. Castro
author: E. M. Rojas
published in: Integral Equations and Operator Theory
publication date: 2011-06-17T00:00:00Z
review text: The paper is organized in seven sections. References are exhaustive and these citations can initiate furthering the research in the directions similar to those given in the paper but with different approach. The fundamental concept that helped the authors to write this paper is the formulation of linear boundary value problems for analytic functions. Singular integral equations with shift are connected with boundary value problems with a shift in a natural way. With all knowledge on these and similar topics and several applications and theories developed, the authors are inspired to reduce a class of singular integral equations with shift on a weighted Lebesgue space to a system of singular integral equations by using some operator identities and projections, by which the solutions of the initial equation throughout a Riemann boundary value problem are studied. The authors avoid the use of the classical method, which allows a direct construction of the corresponding solutions. Therefore, the equations under study are associated with a system of pure singular integral equations. In the final part of the paper weighted Carleman shift operators of commutative and anti-commutative types are considered.
reviewed by: P. K. Banerji
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45F15
zbMATH DE Number: 5909271
zbMATH Keywords: system of singular integral equation
zbMATH Keywords: reflection
zbMATH Keywords: solvability
zbMATH Keywords: Riemann boundary value problem
zbMATH Keywords: unit circle
zbMATH Keywords: Carleman shift
MaRDI profile type: Publication
full work available at URL: s00020-011-1871-6
OpenAlex ID: W1996029440
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DOI: 10.1007/S00020-011-1871-6
description: scientific article; zbMATH DE number 5909271