What question did this study set out to answer?

The aim is to explore the uniqueness in recovering Sturm–Liouville operators using spectral boundary conditions.

February 21, 2026Lobachevskii Journal of Mathematics0 citations

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

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, ) by a single spectrum, if the potential is given on the interval (0, 2). Moreover, applying Gesztesy–Simon’s theorem and Weyl function technique, and knowing the potential on the interval (0, /2 (1-) ) as (0, 1), a finite set of eigenvalues determines the potential on (0, ).

Ask AI

Helpful

Bookmark

View Full Paper