Uniqueness theorem for inverse scattering problem with non-overdetermined data

Details Uniqueness theorem for inverse scattering problem with non-overdetermined data Uniqueness theorem for inverse scattering problem with non-overdetermined data

2009-10-29

arxiv.org/abs/0910.5731v1

Physics

Mathematical Physics

Scientific paper

Let $q(x)$ be real-valued compactly supported sufficiently smooth function,
$q\in H^\ell_0(B_a)$, $B_a:=\{x: |x|\leq a, x\in R^3$ . 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 $q$.

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