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Title: Diffraction from polygonal-conical screens, an operator approach
Author: Castro, Luís P.
Duduchava, Roland
Speck, Frank-Olme
Keywords: Diffraction
Plane screen
Polygonal domain
Conical domain
Dirichlet problem
Neumann problem
Explicit solution
Wiener-Hopf operator
Sobolev space
Matrical coupling
Orthogonal projector
Issue Date: 26-Apr-2014
Publisher: Springer Basel
Abstract: 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 polynomial-conical 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 So\-bo\-lev 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.
DOI: 10.1007/978-3-0348-0816-3_6
ISBN: 978-3-0348-0815-6
Appears in Collections:CIDMA - Capítulo de livro
FAAG - Capítulo de livro

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