Finite-part singular integral approximations in Hilbert spaces

E. G. Ladopoulos, G. Tsamasphyros and V. A. Zisis

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-7

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:830730

DOI: 10.1155/S016117120431135X

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