On the Hald-Gesztesy-Simon theorem
For the boundary value problem \[ -y''+q(x)y=\lambda y,\quad y'(0)-H_1y(0)=y'(a)+H_2y(a)=0, \] the inverse problem of recovering \(q(x)\), \(x\in(a/2,a]\) and \(H_2\) is studied when the potential \(q(x)\), \(x\in[0,a/2]\), the coefficient \(H_1\) and the spectrum are known a priori. Sufficient conditions for the solvability of this inverse problem are established.
scientific article; zbMATH DE number 6121607
scientific article