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Properties of far-field operators in acoustic scattering. (English) Zbl 0692.35072

From the author’s abstract. The far-field operator for an exterior boundary value problem for the Helmholtz equation maps the boundary data onto the far-field pattern of the solution. This paper computes the \(L^ 2\)-adjoint of this operator for various choices of boundary conditions. In scattering theory the boundary data are given by the traces of plane waves. The author characterizes the closure of the span of the images of these plane waves under the far field operator.
Finally, the results are extended to more general topologies including Sobolev and Hölder norms.
Reviewer: T.R.Faulkner

MSC:

35P25 Scattering theory for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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