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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators


Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 124 (1996), 1177-1182
MSC (1991): Primary 47B39, 05C50, 35P05, 58C40
MathSciNet review: 1307565
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Abstract | References | Similar Articles | Additional Information

Abstract: Examples are constructed of Laplace-Beltrami operators and graph Laplacians with singular continuous spectrum.


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  • [1] René Carmona, Abel Klein, and Fabio Martinelli, Anderson localization for Bernoulli and other singular potentials, Comm. Math. Phys. 108 (1987), no. 1, 41–66. MR 872140 (88f:82027)
  • [2] R. del Rio, S. Jitomirskaya, Y. Last, and B. Simon, Operators with singular continuous spectrum, IV. Hausdorff dimension and rank one perturbations, in preparation.
  • [3] R. del Rio, N. Makarov, and B. Simon, Operators with singular continuous spectrum, II. Rank one operators, Commun. Math. Phys. 165 (1994), 59--67. CMP 95:02
  • [4] V. Jakšić, S. Molčanov, and B. Simon, Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps, J. Funct. Anal. 106 (1992), no. 1, 59–79. MR 1163464 (93f:35165), http://dx.doi.org/10.1016/0022-1236(92)90063-O
  • [5] S. Jitomirskaya and B. Simon, Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators, Commun. Math. Phys. 165 (1994), 201--205. CMP 95:02
  • [6] B. Simon, Operators with singular continuous spectrum, I. General operators, Ann. Math. 141 (1995), 131--145.
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    Math. Soc. 123 (1995), 3749--3755.
  • [8] B. Simon and G. Stolz, Operators with singular continuous spectrum, V. Sparse potentials, Proc. Amer. Math. Soc. (to appear).

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Additional Information

Barry Simon
Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 253-37, Pasadena, California 91125

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03245-5
PII: S 0002-9939(96)03245-5
Received by editor(s): October 7, 1994
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 Barry Simon