On the denseness of the set of scattering amplitudes

Abstract

It is proved that the set of scattering amplitudes $\{A(\beta ,\alpha ,k){\}}_{\forall \alpha \in S^2}$, known for all $\beta \in S^2$, 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 $A(\beta ,\alpha ,k)$ is the scattering amplitude corresponding to an obstacle $D$, where $D\subset {\mathbb{R}}^3$ is a bounded domain with a boundary $S$. The boundary condition on $S$ is the Dirichlet condition.

References in corpus (1)

• Completeness of the set of scattering amplitudes