A Borg-Levinson theorem for Bessel operators

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 -y ''(x) + m(m+1)y(x)/x(2) + p(x)y(x) = lambda y(z), on the unit interval subject to various boundary conditions. This result is used to show that even zonal Schrodinger operators and Laplace operators on spheres are uniquely determined by a subsequence of their eigenvalues.