Cantor singular continuous spectrum for operators along interval exchange transformations
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- by M. Cobo, C. Gutierrez and C. R. de Oliveira PDF
- Proc. Amer. Math. Soc. 136 (2008), 923-930 Request permission
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.References
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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
- MR Author ID: 206915
- Email: oliveira@dm.ufscar.br
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 923-930
- MSC (2000): Primary 47B36, 47B37, 37B05, 37B10
- DOI: https://doi.org/10.1090/S0002-9939-07-09074-0
- MathSciNet review: 2361865