Method of Hyperelliptic Surfaces for Vector Functional-Difference Equations
A vector functional-difference equation of the first order with a special matrix coeffcient 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 hyperelliptic 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. As an example, a new model problem for an anisotropic half-plane with imperfect interfaces which are illuminated by a plane electromagnetic wave at oblique incidence, is considered.
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