Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpinski gasket
Open Access
- 29 March 2007
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 135 (8) , 2453-2459
Abstract
In this note we investigate the asymptotic behavior of spectra of Schrödinger operators with continuous potential on the Sierpiński gasket S G SG . In particular, using the existence of localized eigenfunctions for the Laplacian on S G SG we show that the eigenvalues of the Schrödinger 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 Schrödinger operators on compact Riemannian manifolds.Keywords
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