Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpinski gasket |
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Authors: | Kasso A Okoudjou Robert S Strichartz |
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Institution: | Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201 ; Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201 |
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Abstract: | In this note we investigate the asymptotic behavior of spectra of Schrödinger operators with continuous potential on the Sierpinski gasket . In particular, using the existence of localized eigenfunctions for the Laplacian on 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. |
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Keywords: | Analysis on fractals Schr\"odinger operators Sierpi\'nski gasket |
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