International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 49-52, Pages 2787-2793
doi:10.1155/S016117120431135X
Finite-part singular integral approximations in Hilbert spaces
E.G. Ladopoulos
, G. Tsamasphyros
and V.A. Zisis
Interpaper Research Organization, 56 Anagnostopoulou Street, Athens 10672, Greece
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.