Rapidly decreasing potentials on a background of finite-zone potentials and the \(\bar\partial\)-problem on Riemann surfaces (Q1813240)

The scattering theory for the operators \(L_ p=\partial_ y-\partial^ 2_ x+u(x,y)\), \(L_ s=-\partial^ 2_ x-\partial^ 2_ y+u(x,y)\) is studied. The energy \({\mathcal E}_ 0\) is fixed and the potential \(u(x,y)\) has the form \(u(x,y)=u_ 0(x,y)+u_ 1(x,y)\), where \(u_ 0(x,y)\) is a finite-zone potential, \(u_ 1 (x,y)\) is a quickly decreasing potential.