Stability of the inverse problem in potential scattering at fixed energy (Q1812951)

We prove an estimate of the kind \(\| q_ 1-q_ 2\|_{L^{\infty}}\leq C\phi (\| A_{q_ 1}-A_{q_ 2}\|_{R,3/2,-1/2})\), where \(A_{q_ i}(\omega,\theta)\), \(i=1,2\) is the scattering amplitude related to the compactly supported potential \(q_ i(x)\) at a fixed energy level \(k=const.\), \(\phi (t)=(-\ln t)^{- \delta}\), \(0<\delta <1\) and \(\| \cdot \|_{R,3/2,-1/2}\) is a suitably defined norm.