Inverse problems for the Hill operator: The direct approach (Q1386567)

The Hill operator \[ H= {d^2\over dx^2}+ V(x),\quad -\infty< x<\infty\tag{1} \] is considered, where \(V(x)= V(x+ 1)\), \(V(x)= V(1- x)\), \(\int^1_0 V(x)dx= 0\). The mapping of potentials \(V(x)\) into the space of spectral data is introduced. The direct approach to the inverse problem for the Hill operator is based on this mapping.