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Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields |
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| Authors: | Durand William APham Ngoc Dinh |
| Institution: | a MAPMO, UMR 6628, Department of Mathematics, Orléans University, BP 6759, 45067 Orléans cedex 2, France b Mathematics Department, College of Natural Sciences, HoChiMinh City National University, 27 Nguyen Van Cu, Distr. 5, HoChiMinh City, Viet Nam |
| Abstract: | An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given. |
| Keywords: | Neumann-Dirichlet conditions Difference-functional equations Cauchy-Carleman equation Hilbert transform |
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