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Complex Analysis and Operator Theory

, Volume 7, Issue 6, pp 1839–1851 | Cite as

Optimal and Approximate Solutions of Singular Integral Equations by Means of Reproducing Kernels

  • L. P. CastroEmail author
  • S. Saitoh
Article

Abstract

A reproducing kernel method is proposed to obtain the optimal and approximate solutions of Carleman singular integral equations. Therefore, we will be mostly interested in singular integral equations with a Cauchy type kernel and whose coefficients are real or complex valued functions. The new method and corresponding concepts allow the analysis of associated discrete singular integral equations and corresponding inverse source problems in appropriate frameworks.

Keywords

Singular integral equation Reproducing kernel Discrete singular integral equation Optimal solution Approximate solution Hilbert transform 

Mathematics Subject Classification (2000)

45E05 45L05 30C40 65R20 

Notes

Acknowledgments

This work was supported in part by FEDER funds through COMPETE-Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690. S. Saitoh is supported in part by the Grant-in-Aid for the Scientific Research (C)(2) (No. 24540113).

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal

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