International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 52, Pages 2787-2793
doi:10.1155/S016117120431135X
Finite-part singular integral approximations in Hilbert spaces
Interpaper Research Organization, 56 Anagnostopoulou Street, Athens 10672, Greece
Received 12 November 2003
Copyright © 2004 E. G. Ladopoulos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.