Inverse Problems 26, 105013, 14pp (2010) [DOI: 10.1088/0266-5611/26/10/105013]

Inverse Eigenvalue Problems for Perturbed Spherical Schrödinger Operators

Aleksey Kostenko, Alexander Sakhnovich, and Gerald Teschl

We investigate the eigenvalues of perturbed spherical Schrödinger operators under the assumption that the perturbation q(x) satisfies x q(x) ∈ L1(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).

MSC2000: Primary 34B20, 34L15; Secondary 81V45 , 47A10
Keywords: Schrödinger operators, spectral theory, strongly singular potentials

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