A Borg–Levinson theorem for Bessel operators

Robert Carlson

Vol. 177 (1997), No. 1, 1–26

DOI: 10.2140/pjm.1997.177.1

Abstract

This paper presents a direct analog of the Borg-Levinson theorem on the recovery of a potential from the sequence of eigenvalues and norming constants for differential equations of the form

on the unit interval subject to various boundary conditions. This result is used to show that even zonal Schrödinger operators and Laplace operators on spheres are uniquely determined by a subsequence of their eigenvalues.

Milestones

Received: 24 May 1995

Revised: 3 October 1995

Published: 1 January 1997