Inverse problems of recovering first-order integro-differential operators from spectra

TL;DR

This paper investigates inverse spectral problems for first-order integro-differential operators, establishing conditions under which the kernel components can be uniquely recovered from spectral data on a finite interval.

Contribution

It provides new uniqueness theorems for recovering kernel components in inverse spectral problems for first-order integro-differential operators.

Findings

Proved uniqueness theorems for inverse spectral problems

Demonstrated recoverability of kernel components from spectral data

Extended inverse problem theory to a new class of operators

Abstract

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for this class of inverse problems.