On a generalization of the three spectral inverse problem

TL;DR

This paper extends the classical three spectral inverse problem by considering additional spectral data from subdivided intervals, enabling the reconstruction of Sturm-Liouville potentials with more complex spectral information.

Contribution

It introduces a generalized framework for the inverse spectral problem using combined spectral data from multiple boundary conditions and subintervals.

Findings

Derived a method to reconstruct potentials from combined spectral data.

Extended classical inverse problem to more complex spectral configurations.

Provided theoretical foundations for potential recovery with partial spectra.

Abstract

We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$, parts of spectra of the Dirichlet-Neumann and Dirichlet-Dirichlet problems on $[0,a/2]$ and parts of spectra of the Dirichlet-Newman and Dirichlet-Dirichlet problems on $[a/2,a]$, we find the potential of the Sturm-Liouville equation.