A new Improvement of Ambarzumyan's Theorem

TL;DR

This paper extends Ambarzumyan's theorem to quasi-periodic boundary value problems, requiring only partial spectral data and relaxing conditions on the first eigenvalue, thus broadening its applicability.

Contribution

It introduces a novel extension of Ambarzumyan's theorem to quasi-periodic problems with partial spectral information and weaker eigenvalue conditions.

Findings

Extended Ambarzumyan's theorem to quasi-periodic problems

Reduced spectral data requirements

Weakened conditions on the first eigenvalue

Abstract

We extend the classical Ambarzumyan's theorem to the quasi-periodic boundary value problems by using only a part knowledge of one spectrum. We also weaken slightly the Yurko's conditions on the first eigenvalue.