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

 

Singular continuous spectrum for a class of nonprimitive substitution Schrödinger operators


Authors: César R. de Oliveira and Marcus V. Lima
Journal: Proc. Amer. Math. Soc. 130 (2002), 145-156
MSC (1991): Primary 81Q10; Secondary 11B85, 47B39
Published electronically: June 8, 2001
MathSciNet review: 1855631
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Abstract: We present a class of discrete Schrödinger operators, with potentials derived from nonprimitive substitutions, that has purely singular continuous spectrum. We give sufficient conditions on the substitution rule assuring singular continuous spectrum, either for a generic set in the hull of the potential or for a set of total invariant measure.


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Additional Information

César R. de Oliveira
Affiliation: Departamento de Matemática – UFSCar, São Carlos, SP, 13560-970 Brazil
Email: oliveira@dm.ufscar.br

Marcus V. Lima
Affiliation: Departamento de Matemática – UFSCar, São Carlos, SP, 13560-970 Brazil, and AFA, Pirassununga, SP, 13630–000 Brazil
Email: lima@dm.ufscar.br

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06148-2
PII: S 0002-9939(01)06148-2
Received by editor(s): May 30, 2000
Published electronically: June 8, 2001
Additional Notes: The first author was partially supported by CNPq (Brazil).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society