The inverse scattering problem on a fixed energy level for two- dimensional Schrödinger operator (Q1188100)

The paper contains a solution of the inverse scattering problem at fixed \(E>0\) for the two-dimensional Schrödinger operator \[ - \Delta\Phi+v(x)\Phi=E\Phi,\quad x\in\mathbb{R}^ 2, \] where \(v(x)\leq Q(E,\varepsilon)(1+| x|)^{-2-\varepsilon}\), \(\varepsilon>0\) and the function \(Q(E,\varepsilon)\) is possessing the properties \(Q(E,\varepsilon)\to\infty\) for \(E\to\infty\), \(Q(E,\varepsilon)\to 0\) for \(E\to 0\).