Uniqueness theorem for inverse scattering problem with non-overdetermined data

Abstract

Let $q(x)$ be real-valued compactly supported sufficiently smooth function, $q\in H_0^{\ell }(B_a)$, $B_a:=\{x:|x|\le a,x\in R^3$ . It is proved that the scattering data $A(-\beta ,\beta ,k)$ $\forall \beta \in S^2$, $\forall k>0$ determine $q$ uniquely. here $A(\beta ,\alpha ,k)$ is the scattering amplitude, corresponding to the potential $q$.

References in corpus (1)

• Stability of solutions to inverse scattering problems with fixed-energy data

Cited by in corpus (2)

• Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave
• Inverse obstacle scattering with non-over-determined data