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Finite-part singular integral approximations in Hilbert spaces

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  • E. G. Ladopoulos
  • G. Tsamasphyros
  • V. A. Zisis

Abstract

Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.

Suggested Citation

  • E. G. Ladopoulos & G. Tsamasphyros & V. A. Zisis, 2004. "Finite-part singular integral approximations in Hilbert spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:830730
    DOI: 10.1155/S016117120431135X
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