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

 

Cantor singular continuous spectrum for operators along interval exchange transformations


Authors: M. Cobo, C. Gutierrez and C. R. de Oliveira
Journal: Proc. Amer. Math. Soc. 136 (2008), 923-930
MSC (2000): Primary 47B36, 47B37, 37B05, 37B10
Published electronically: November 30, 2007
MathSciNet review: 2361865
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Abstract: It is shown that Schrödinger operators, with potentials along the shift embedding of Lebesgue almost every interval exchange transformations, have Cantor spectrum of measure zero and pure singular continuous for Lebesgue almost all points of the interval.


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Additional Information

M. Cobo
Affiliation: Departamento de Matemática, UFES, Av. F. Ferrari 514, Vitória, ES, 19075-910 Brazil
Email: miltonc@cce.ufes.br

C. Gutierrez
Affiliation: Departamento de Matemática, ICMC/USP, CxP 668, São Carlos, SP, 13560-970 Brazil
Email: gutp@icmc.usp.br

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

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09074-0
PII: S 0002-9939(07)09074-0
Keywords: Schr\"odinger operator, interval exchange transformation, singular continuous spectrum, Cantor spectrum.
Received by editor(s): June 12, 2006
Received by editor(s) in revised form: October 23, 2006
Published electronically: November 30, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society