dc.contributor.author | İdemen, Mehmet Mithat | en_US |
dc.contributor.author | Alkumru, Ali | en_US |
dc.date.accessioned | 2015-01-15T22:59:58Z | |
dc.date.available | 2015-01-15T22:59:58Z | |
dc.date.issued | 2003-12 | |
dc.identifier.citation | İdemen, M. M. & Alkumru, A. (2003). On a class of functional equations of the wiener-hopf type and their applications in n-part scattering problems. IMA Journal of Applied Mathematics, 68(6), 563-586. doi:10.1093/imamat/68.6.563 | en_US |
dc.identifier.issn | 0272-4960 | |
dc.identifier.issn | 1464-3634 | |
dc.identifier.uri | https://hdl.handle.net/11729/121 | |
dc.identifier.uri | http://dx.doi.org/10.1093/imamat/68.6.563 | |
dc.description | This work was partly supported by the Turkish Academy of Sciences (TUBA). The authors are indebted to a referee who informed them of some references and made valuable suggestions. | en_US |
dc.description.abstract | An asymptotic theory for the functional equation K-phi=f, where K : X-->Y stands for a matrix-valued linear operator of the form K=K1P1+K2P2+...+KnPn, is developed. Here X and Y refer to certain Hilbert spaces, {P-alpha} denotes a partition of the unit operator in X while K-alpha are certain operators from X to Y. One assumes that the partition {P-alpha} as well as the operators K-alpha depend on a complex parameter nu such that all K-alpha are multi-valued around certain branch points at nu=k(+) and nu=k(-) while the inverse operators K-alpha(-1) exist and are bounded in the appropriately cut nu-plane except for certain poles. Then, for a class of {P-alpha} having certain analytical properties, an asymptotic solution valid for \k(+/-)\-->infinity is given. The basic idea is the decomposition of phi into a sum of projections on n mutually orthogonal subspaces of X. The results can be extended in a straightforward manner to the cases of no or more branch points. If there is no branch point or n=2, then the results are all exact. The theory may have effective applications in solving some direct and inverse multi-part boundary-value problems connected with high-frequency waves. An illustrative example shows the applicability as well as the effectiveness of the method. | en_US |
dc.description.sponsorship | Türkiye Bilimler Akademisi | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Oxford Univ Press | en_US |
dc.relation.isversionof | 10.1093/imamat/68.6.563 | |
dc.rights | info:eu-repo/semantics/closedAccess | en_US |
dc.subject | Mixed boundary-value problems | en_US |
dc.subject | Matrix Wiener-Hopf equation | en_US |
dc.subject | Diffraction of high-frequency waves | en_US |
dc.subject | Diffraction | en_US |
dc.subject | Factorization | en_US |
dc.subject | Field | en_US |
dc.subject | Integral equations | en_US |
dc.subject | High-frequency waves | en_US |
dc.subject | Functional equations | en_US |
dc.subject | Poles and zeros | en_US |
dc.subject | Matrix algebra | en_US |
dc.subject | Mathematical operators | en_US |
dc.subject | Frequencies | en_US |
dc.subject | Boundary value problems | en_US |
dc.subject | Approximation theory | en_US |
dc.title | On a class of functional equations of the Wiener-Hopf type and their applications in n-part scattering problems | en_US |
dc.type | article | en_US |
dc.description.version | Publisher's Version | en_US |
dc.relation.journal | IMA Journal of Applied Mathematics | en_US |
dc.contributor.department | Işık Üniversitesi, Mühendislik Fakültesi, Elektrik-Elektronik Mühendisliği Bölümü | en_US |
dc.contributor.department | Işık University, Faculty of Engineering, Department of Electrical-Electronics Engineering | en_US |
dc.contributor.authorID | 0000-0002-1225-7482 | |
dc.identifier.volume | 68 | |
dc.identifier.issue | 6 | |
dc.identifier.startpage | 563 | |
dc.identifier.endpage | 586 | |
dc.peerreviewed | Yes | en_US |
dc.publicationstatus | Published | en_US |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
dc.contributor.institutionauthor | İdemen, Mehmet Mithat | en_US |
dc.relation.index | WOS | en_US |
dc.relation.index | Scopus | en_US |
dc.relation.index | Science Citation Index Expanded (SCI-EXPANDED) | en_US |
dc.description.quality | Q3 | |
dc.description.wosid | WOS:000186446900001 | |