An inverse Sturm-Liouville problem by three spectra
Let \(\{\lambda_{nj}\}_{n\geq 0}\), \(j=1,2,3\), be the eigenvalues to the boundary value problems \(L_j\) for the Sturm-Liouville equation \[ -y''+q(x)y=\lambda y \] with the boundary conditions \(y(0)=y(a)=0,\) \(y(0)=y(a/2)=0\) and \(y(a/2)=y(a)=0\), respectively. Under additional restrictions on the spectra the author studies the inverse problem of recovering \(q\) from the given three spectra \(\{\lambda_{nj}\}_{n\geq 0}\), \(j=1,2,3,\) and provide sufficient conditions for the solvability of this inverse problem.
scientific article; zbMATH DE number 1333095