Asian Journal of Mathematics and Computer Research

AN INVERSE RESULT FOR THE PERIODIC BOUNDARY CONDITIONS

ALP ARSLAN KIRAÇ *

Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University, 20070 Denizli, Turkey

*Author to whom correspondence should be addressed.

---

Abstract

We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operator L with real-valued potential q ∈ L¹[0, 1] and periodic boundary conditions when the subset of the spectrum of L and Fourier coecients c_k of the potential q such that the condition  holds are given. The same result holds for the anti-periodic boundary conditions.

Keywords: Ambarzumyan theorem, inverse spectral theory, Hill operator, eigenvalue asymptotics

---

---