Finite-part singular integral approximations in Hilbert spaces
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120431135X |
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| _version_ | 1832548863725010944 |
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| author | E. G. Ladopoulos G. Tsamasphyros V. A. Zisis |
| author_facet | E. G. Ladopoulos G. Tsamasphyros V. A. Zisis |
| author_sort | E. G. Ladopoulos |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-133e381eedc84fe7885f742d24496f75 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-133e381eedc84fe7885f742d24496f752025-02-03T06:12:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004522787279310.1155/S016117120431135XFinite-part singular integral approximations in Hilbert spacesE. G. Ladopoulos0G. Tsamasphyros1V. A. Zisis2Interpaper Research Organization, 56 Anagnostopoulou Street, Athens 10672, GreeceInterpaper Research Organization, 56 Anagnostopoulou Street, Athens 10672, GreeceInterpaper Research Organization, 56 Anagnostopoulou Street, Athens 10672, GreeceSome 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.http://dx.doi.org/10.1155/S016117120431135X |
| spellingShingle | E. G. Ladopoulos G. Tsamasphyros V. A. Zisis Finite-part singular integral approximations in Hilbert spaces International Journal of Mathematics and Mathematical Sciences |
| title | Finite-part singular integral approximations in Hilbert spaces |
| title_full | Finite-part singular integral approximations in Hilbert spaces |
| title_fullStr | Finite-part singular integral approximations in Hilbert spaces |
| title_full_unstemmed | Finite-part singular integral approximations in Hilbert spaces |
| title_short | Finite-part singular integral approximations in Hilbert spaces |
| title_sort | finite part singular integral approximations in hilbert spaces |
| url | http://dx.doi.org/10.1155/S016117120431135X |
| work_keys_str_mv | AT egladopoulos finitepartsingularintegralapproximationsinhilbertspaces AT gtsamasphyros finitepartsingularintegralapproximationsinhilbertspaces AT vazisis finitepartsingularintegralapproximationsinhilbertspaces |