On a class of functional equations of the Wiener-Hopf type and their applications in n-part scattering problems
Yükleniyor...
Dosyalar
Tarih
2003-12
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Oxford Univ Press
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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.
Açıklama
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.
Anahtar Kelimeler
Mixed boundary-value problems, Matrix Wiener-Hopf equation, Diffraction of high-frequency waves, Diffraction, Factorization, Field, Integral equations, High-frequency waves, Functional equations, Poles and zeros, Matrix algebra, Mathematical operators, Frequencies, Boundary value problems, Approximation theory
Kaynak
IMA Journal of Applied Mathematics
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
68
Sayı
6
Künye
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
