Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpinski gasket
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- by Kasso A. Okoudjou and Robert S. Strichartz PDF
- Proc. Amer. Math. Soc. 135 (2007), 2453-2459 Request permission
Abstract:
In this note we investigate the asymptotic behavior of spectra of Schrödinger operators with continuous potential on the Sierpiński gasket $SG$. In particular, using the existence of localized eigenfunctions for the Laplacian on $SG$ 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.References
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Additional Information
- Kasso A. Okoudjou
- Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
- Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
- MR Author ID: 721460
- ORCID: setImmediate$0.18192135121667974$6
- Email: kasso@math.umd.edu
- Robert S. Strichartz
- Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
- Email: str@math.cornell.edu
- Received by editor(s): January 9, 2006
- Published electronically: March 29, 2007
- Additional Notes: The research of the second author was supported in part by the National Science Foundation, grant DMS-0140194.
- Communicated by: Michael T. Lacey
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2453-2459
- MSC (2000): Primary 35P20, 28A80; Secondary 42C99, 81Q10
- DOI: https://doi.org/10.1090/S0002-9939-07-09008-9
- MathSciNet review: 2302566