On the denseness of the set of scattering amplitudes

It is proved that the set of scattering amplitudes ${A(\beta, \alpha, k)}_{\forall \alpha \in S^2}$,knownforall$\beta\in S^2$,where$S^2$ is the unit sphere in ${\mathbb{R}}^3$, $k>0$ is fixed, $k^2$ is not a Dirichlet eigenvalue of the Laplacian in $D$, is dense in $L^2(S^2)$. Here $A(\beta, \alpha, k)$isthescatteringamplitudecorrespondingtoanobstacle$D$,where$D\subset $\mathbb{R}$^3$isaboundeddomainwithaboundary$S$. The boundary condition on $S$ is the Dirichlet condition.