Singular continuous limiting eigenvalue distributions for Schrödinger operators on a 2-sphere (Q1815299)

The authors consider the Schrödinger operator \(H\) with continuous potential on the two-dimensional unit sphere. They first give a new proof of the limiting distribution theorem, which asserts that the eigenvalues of \(H\) in the \(\ell\)th cluster have a limiting distribution as \(\ell\to\infty\). Then, they provide examples for which this limiting distribution is singular continuous. The construction of these examples relies on a preliminary discussion of the Radon transform and its inverse.