On a class of functional equations of the Wiener-Hopf type and their applications in n-part scattering problems

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dc.authorid0000-0002-1225-7482
dc.authorid0000-0001-5290-849X
dc.contributor.authorİdemen, Mehmet Mithaten_US
dc.contributor.authorAlkumru, Alien_US
dc.date.accessioned2015-01-15T22:59:58Z
dc.date.available2015-01-15T22:59:58Z
dc.date.issued2003-12
dc.departmentIşık Üniversitesi, Mühendislik Fakültesi, Elektrik-Elektronik Mühendisliği Bölümüen_US
dc.departmentIşık University, Faculty of Engineering, Department of Electrical-Electronics Engineeringen_US
dc.descriptionThis 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.abstractAn 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.sponsorshipTürkiye Bilimler Akademisien_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationİdemen, 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/68.6.563en_US
dc.identifier.doi10.1093/imamat/68.6.563
dc.identifier.endpage586
dc.identifier.issn0272-4960
dc.identifier.issn1464-3634
dc.identifier.issue6
dc.identifier.scopus2-s2.0-0344012940
dc.identifier.scopusqualityQ3
dc.identifier.startpage563
dc.identifier.urihttps://hdl.handle.net/11729/121
dc.identifier.urihttp://dx.doi.org/10.1093/imamat/68.6.563
dc.identifier.volume68
dc.identifier.wosWOS:000186446900001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakScience Citation Index Expanded (SCI-EXPANDED)en_US
dc.institutionauthorİdemen, Mehmet Mithaten_US
dc.institutionauthorid0000-0002-1225-7482
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherOxford Univ Pressen_US
dc.relation.ispartofIMA Journal of Applied Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectMixed boundary-value problemsen_US
dc.subjectMatrix Wiener-Hopf equationen_US
dc.subjectDiffraction of high-frequency wavesen_US
dc.subjectDiffractionen_US
dc.subjectFactorizationen_US
dc.subjectFielden_US
dc.subjectIntegral equationsen_US
dc.subjectHigh-frequency wavesen_US
dc.subjectFunctional equationsen_US
dc.subjectPoles and zerosen_US
dc.subjectMatrix algebraen_US
dc.subjectMathematical operatorsen_US
dc.subjectFrequenciesen_US
dc.subjectBoundary value problemsen_US
dc.subjectApproximation theoryen_US
dc.titleOn a class of functional equations of the Wiener-Hopf type and their applications in n-part scattering problemsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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