Diffraction from Polygonal-conical Screens, an Operator Approach

  • Luís P. CastroEmail author
  • Roland Duduchava
  • Frank-Olme Speck
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 242)


The aim of this work is to construct explicitly resolvent operators for a class of boundary value problems in diffraction theory. These are formulated as boundary value problems for the three-dimensional Helmholtz equation with Dirichlet or Neumann conditions on a plane screen of polynomialconical form (including unbounded and multiply-connected screens), in weak formulation. The method is based upon operator theoretical techniques in Hilbert spaces, such as the construction of matrical coupling relations and certain orthogonal projections, which represent new techniques in this area of applications. Various cross connections are exposed, particularly considering classical Wiener–Hopf operators in Sobolev spaces as general Wiener–Hopf operators in Hilbert spaces and studying relations between the crucial operators in game. Former results are extended, particularly to multiply-connected screens.


Diffraction plane screen polygonal domain conical domain Dirichlet problem Neumann problem explicit solution Wiener–Hopf operator Sobolev space matrical coupling orthogonal projector 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Luís P. Castro
    • 1
    Email author
  • Roland Duduchava
    • 2
  • Frank-Olme Speck
    • 3
  1. 1.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  2. 2.Andrea Razmadze Mathematical InstituteIvane Javakhishvili State UniversityTbilisiGeorgia
  3. 3.Centro de Análise Funcional e Aplicações Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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