Aleksey Kostenko, Alexander Sakhnovich, ad Gerald Teschl
Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
(44K, LaTeX2e)
ABSTRACT. We investigate the eigenvalues of perturbed spherical Schr\"odinger operators under the
assumption that the perturbation $q(x)$ satisfies $x q(x) \in L^1(0,1)$. We show that the
square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues
up to an decaying error depending on the behavior of $q(x)$ near $x=0$. Furthermore,
we provide sets of spectral data which uniquely determine $q(x)$.