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

**[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****[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**, 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.**[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:
http://dx.doi.org/10.1090/S0002-9939-96-03245-5

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