# An Extension of The First Eigen-type Ambarzumyan theorem

## TL;DR

This paper extends the first eigenvalue-type Ambarzumyan theorem to arbitrary self-adjoint Sturm-Liouville operators, contributing to inverse spectral theory and broadening the theorem's applicability.

## Contribution

It generalizes Ambarzumyan's theorem for a wider class of Sturm-Liouville operators, enhancing inverse spectral analysis methods.

## Key findings

- Extended Ambarzumyan's theorem to arbitrary self-adjoint Sturm-Liouville operators
- Provided new insights into inverse spectral theory
- Broadened the applicability of eigenvalue-based spectral characterizations

## Abstract

An extension of the first eigenvalue-type Ambarzumyan's theorem are provided for the arbitrary self-adjoint Sturm-Liouville differential operators. The result makes a contribution to the P\"oschel-Trubowitz inverse spectral theory as well.