On Uniqueness of Recovering of Sturm–Liouville Operators with the Spectral Boundary Condition

The paper focuses on the Sturm–Liouville type differential equation with spectral boundary conditions defined over a finite interval. It employs the Hochstadt–Lieberman method alongside the Weyl function technique to get the potential on the interval (0,π) by a single spectrum, if the potential is given on the interval (0,π/2) . Moreover, applying Gesztesy–Simon’s theorem and Weyl function technique, and knowing the potential on the interval (0,π/2(1-β)) as β∈(0,1) , a finite set of eigenvalues determines the potential on (0,π) .