© 2000 by Oxford University Press
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A generalization of the Wiener–Hopf approach to direct and inverse scattering problems connected with non-homogeneous half-spaces bounded by n-part boundaries
( 1 ISIK University, Büyükdere caddesi, Maslak 80670, Istanbul, Turkey 2 Gebze Institute of Technology, Department of Electronics Engineering, Gebze, Kocaeli, Turkey )
The classical Wiener–Hopf method connected with mixed two-part boundary-value problems is generalized to cover n-part boundaries. To this end one starts from an ad-hoc representation for the Green function, which involves nunknown functions having certain analytical properties. Thus the problem is reduced to a functional equation involving nunknowns, which constitutes a generalization of the classical Wiener–Hopf equation in two unknowns. To solve this latter which cannot be solved exactly when n 
3, one establishes a new method permitting one to obtain the asymptotic expressions valid when the wavelength is sufficiently small as compared with the widths of the inner strips of the boundary. The essentials of the method are elucidated through a concrete inverse scattering problem whose aim is to determine the constitutive electromagnetic parameters of a slab and a half-space bounded by an n-part impedance plane. Some illustrative numerical examples show the applicability as well as the accuracy of the method.
Key Words: Wiener–Hopf technique; Mixed Boundary-Value Problems; Inverse Scattering
Received 10 May, 1999. Revised 27 November, 1999.
Present address: School of Mathematical Sciences, North Park Road, University of Exeter, Exeter, Devon EX4 4QE. 
drew@maths.exeter.ac.uk