Recovering Differential Operators with Nonlocal Boundary Conditions

TL;DR

This paper investigates inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions, introducing generalized spectral characteristics and proving uniqueness theorems for their inverse reconstruction.

Contribution

It introduces generalized Weyl-type functions and spectra for nonlocal boundary conditions and proves their uniqueness in inverse spectral problems.

Findings

Uniqueness theorems for inverse problems using Weyl-type functions

Uniqueness theorems using two spectra

Generalization of classical inverse spectral results

Abstract

Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the well-known Weyl function and Borg's inverse problem for the classical Sturm-Liouville operator. Two uniqueness theorems of inverse problems from the Weyl-type function and two spectra are presented and proved, respectively.