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Factorization of a class of matrices generated by Sommerfeld diffraction problems with oblique derivatives
Author(s) -
Lebre A. B.,
Moura Santos A.,
Speck F.O.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970925)20:14<1185::aid-mma909>3.0.co;2-t
Subject(s) - mathematics , factorization , oblique case , operator (biology) , matrix (chemical analysis) , inverse , matrix decomposition , fourier transform , pure mathematics , algebra over a field , mathematical analysis , geometry , eigenvalues and eigenvectors , algorithm , philosophy , linguistics , biochemistry , chemistry , materials science , repressor , quantum mechanics , physics , transcription factor , composite material , gene
An explicit factorization of the Fourier symbol matrix functions generated by Sommerfeld diffraction problems with oblique derivatives is obtained. For this purpose a new prefactorization procedure is developed which makes use of factorization through weighted L 2 spaces. These results yield a representation of a generalized inverse of the corresponding matrix Wiener–Hopf operator and the asymptotic behaviour of the solution at the edge of the screen. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.