# Recovering First Order Integro-Differential Operators from Spectral Data

## TL;DR

This paper investigates the spectral properties of first order integro-differential operators on finite intervals and proves a uniqueness theorem for their inverse problem, enabling operator reconstruction from spectral data.

## Contribution

It establishes spectral properties and proves a uniqueness theorem for recovering first order integro-differential operators from spectral data.

## Key findings

- Spectral characteristics of the operators are characterized.
- A uniqueness theorem for the inverse problem is proved.
- Operators can be uniquely recovered from spectral data.

## Abstract

First order integro-differential operators on a finite interval are studied. Properties of spectral characteristic are established, and the uniqueness theorem is proved for the inverse problem of recovering operators from their spectral data.