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

Key Points

• The aim is to explore the uniqueness in recovering Sturm–Liouville operators using spectral boundary conditions.
• Utilized Hochstadt–Lieberman method for potential recovery
• Employed Weyl function technique to link spectra to potential
• Applied Gesztesy–Simon theorem for defining potentials based on given intervals
• Showed that the potential can be recovered uniquely from a single spectrum on the interval (0, π)
• Defined potential on (0, π) using knowledge from eigenvalues over (0, π/2(1-β))
• Confirmed a finite set of eigenvalues can effectively determine the potential in the specified intervals

Abstract