SINGULAR CONTINUOUS LIMITING EIGENVALUE DISTRIBUTIONS FOR SCHRODINGER-OPERATORS ON A 2-SPHERE

Let H=-Delta+V be a Schrodinger operator acting in L(2)(S), with S the two-dimensional unit sphere, Delta the spherical Laplacian, and V a c ontinuous potential. As is well known, the eigenvalues of H in the lth cluster, i.e., those eigenvalues within a radius sup /V/ of l(l+1), t he lth eigenvalue of -Delta, have a limiting distribution; l-->infinit y. We provide an alternative self-contained proof of this fact. We the n exhibit Holder continuous potentials V, both axially- and nonaxially -symmetric, for which the limiting distributions are singular continuo us. (C) 1996 Academic Press, Inc.