Inverse problems for the Hill operator: The direct approach
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.
scientific article; zbMATH DE number 1155287