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Cantor singular continuous spectrum for operators along interval exchange transformations
Author(s):
M.
Cobo;
C.
Gutierrez;
C.
R.
de Oliveira
Journal:
Proc. Amer. Math. Soc.
136
(2008),
923-930.
MSC (2000):
Primary 47B36, 47B37, 37B05, 37B10
Posted:
November 30, 2007
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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.
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
Email:
oliveira@dm.ufscar.br
DOI:
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
Posted:
November 30, 2007
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
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