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Integral Equations and Operator Theory

, Volume 70, Issue 1, pp 63–99 | Cite as

On the Solvability of Singular Integral Equations with Reflection on the Unit Circle

  • L. P. CastroEmail author
  • E. M. Rojas
Article

Abstract

The solvability of a class of singular integral equations with reflection in weighted Lebesgue spaces is analyzed, and the corresponding solutions are obtained. The main techniques are based on the consideration of certain complementary projections and operator identities. Therefore, the equations under study are associated with systems of pure singular integral equations. These systems will be then analyzed by means of a corresponding Riemann boundary value problem. As a consequence of such a procedure, the solutions of the initial equations are constructed from the solutions of Riemann boundary value problems. In the final part of the paper, the method is also applied to singular integral equations with the so-called commutative and anti-commutative weighted Carleman shifts.

Mathematics Subject Classification (2010)

Primary 45E05 Secondary 30E20 30E25 45E10 47A68 47G10 

Keywords

Singular integral equation reflection shift solvability Riemann boundary value problem 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Departamento de MatemáticasPontificia Universidad JaverianaBogotáColombia

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