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

Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators
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by Barry Simon PDF

Proc. Amer. Math. Soc. 124 (1996), 1177-1182

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

References

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
R. del Rio, S. Jitomirskaya, Y. Last, and B. Simon, Operators with singular continuous spectrum, IV. Hausdorff dimension and rank one perturbations, in preparation.
R. del Rio, N. Makarov, and B. Simon, Operators with singular continuous spectrum, II. Rank one operators, Commun. Math. Phys. 165 (1994), 59–67.
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, DOI 10.1016/0022-1236(92)90063-O
S. Jitomirskaya and B. Simon, Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators, Commun. Math. Phys. 165 (1994), 201–205.
B. Simon, Operators with singular continuous spectrum, I. General operators, Ann. Math. 141 (1995), 131–145.
—, $L^{p}$ norms of the Borel transform and the decomposition of measures, Proc. Amer. Math. Soc. 123 (1995), 3749–3755.
B. Simon and G. Stolz, Operators with singular continuous spectrum, V. Sparse potentials, Proc. Amer. Math. Soc. (to appear).