Diffraction from Polygonal-conical Screens, an Operator Approach

Abstract

AbstractThe 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.KeywordsDiffractionplane screenpolygonal domainconical domainDirichlet problemNeumann problemexplicit solutionWiener–Hopf operatorSobolev spacematrical couplingorthogonal projector