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Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators
Author(s):
Barry
Simon
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1177-1182.
MSC (1991):
Primary 47B39, 05C50, 35P05, 58C40
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Abstract:
Examples are constructed of Laplace-Beltrami operators and graph Laplacians with singular continuous spectrum.
References:
- [1]
- R. Carmona, A. Klein, and F. Martinelli, Anderson localization for Bernoulli and other singular potentials, Commun. Math. Phys. 108 (1987), 41--66. MR 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. Jaksic, S. Molchanov, and B. Simon, Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps, J. Funct. Anal. 106 (1992), 59--79. MR 93f:35165
- [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.
- [7]
- ------,
 norms of the Borel transform and the decomposition of measures, Proc. Amer.
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:
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
Copyright of article:
Copyright
1996,
Barry Simon
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