Vector functional-difference equation in electromagnetic scattering

@article{Antipov2004VectorFE,
  title={Vector functional-difference equation in electromagnetic scattering},
  author={Yuri A. Antipov and V. V. Silvestrov},
  journal={Ima Journal of Applied Mathematics},
  year={2004},
  volume={69},
  pages={27-69}
}
A vector functional-difference equation of the first order with a special matrix coefficient is analysed. It is shown how it can be converted into a Riemann-Hilbert boundary-value problem on a union of two segments on a hyper-elliptic surface. The genus of the surface is defined by the number of zeros and poles of odd order of a characteristic function in a strip. An even solution of a symmetric Riemann-Hilbert problem is also constructed. This is a key step in the procedure for diffraction… 

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