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 $$(0,\pi)$$ by a single spectrum, if the potential is given on the interval $$\left(0,\frac{\pi}{2}\right)$$ . Moreover, applying Gesztesy–Simon’s theorem and Weyl function technique, and knowing the potential on the interval $$(0,\pi/2(1-\beta))$$ as $$\beta\in(0,1)$$ , a finite set of eigenvalues determines the potential on $$(0,\pi)$$ .