Asymptotics of eigenvalue clusters for Schrodinger operators on the Sierpinski gasket

In this note we investigate the asymptotic behavior of spectra of Schrodinger operators with continuous potential on the Sierpinski gasket SG. In particular, using the existence of localized eigenfunctions for the Laplacian on SG we show that the eigenvalues of the Schrodinger operator break into clusters around certain eigenvalues of the Laplacian. Moreover, we prove that the characteristic measure of these clusters converges to a measure. Results similar to ours were first observed by A. Weinstein and V. Guillemin for Schrodinger operators on compact Riemannian manifolds.