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Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpinski gasket
Author(s):
Kasso
A.
Okoudjou;
Robert
S.
Strichartz
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2453-2459.
MSC (2000):
Primary 35P20, 28A80;
Secondary 42C99, 81Q10
Posted:
March 29, 2007
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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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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
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
DOI:
10.1090/S0002-9939-07-09008-9
PII:
S 0002-9939(07)09008-9
Keywords:
Analysis on fractals,
Schr\"odinger operators,
Sierpi\'nski gasket
Received by editor(s):
January 9, 2006
Posted:
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 of article:
Copyright
2007,
American Mathematical Society
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