Method of Hyperelliptic Surfaces for Vector Functional-Difference Equations

  • Y. A. Antipov
  • Silvestrov V. V. 
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)


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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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Y. A. Antipov
    • 1
  • Silvestrov V. V. 
    • 2
  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  2. 2.Department of MathematicsChuvash State UniversityCheboksaryRussia

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