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A Borg-Levinson theorem for Bessel operators. (English) Zbl 0868.34061

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)=λy(x),

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.

MSC:
34L05General spectral theory for OD operators
34L40Particular ordinary differential operators
34B24Sturm-Liouville theory