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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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