Dense Sets and Far Field Patterns in Acoustic Wave Propagation
DAVID L. COLTON, Andreas Kirsch · SIAM Journal on Mathematical Analysis · 1984
We consider the Dirichlet, Neumann, and transmission boundary value problems corresponding to the scattering of an entire, time harmonic acoustic wave by a bounded obstacle in the plane. We first construct sets of solutions to these problems such that the restrictions of these solutions to the boundary $\partial \Omega $ of the scattering obstacle are dense in $L^2 (\partial \Omega )$. These results are then used to determine when the class of far field patterns corresponding to each of these scattering problems is dense or not dense in $L^2 [0,2\pi ]$.