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

 

Operators with singular continuous spectrum, V. Sparse potentials


Authors: B. Simon and G. Stolz
Journal: Proc. Amer. Math. Soc. 124 (1996), 2073-2080
MSC (1991): Primary 34L40, 34B24
MathSciNet review: 1342046
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Abstract | References | Similar Articles | Additional Information

Abstract: By presenting simple theorems for the absence of positive eigenvalues for certain one-dimensional Schrödinger operators, we are able to construct explicit potentials which yield purely singular continuous spectrum.


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Additional Information

B. Simon
Affiliation: Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125-0001
Email: bsimon@caltech.edu

G. Stolz
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170
Email: stolz@vorteb.math.uab.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03465-X
PII: S 0002-9939(96)03465-X
Received by editor(s): January 9, 1995
Additional Notes: This material is based upon work supported by the National Science Foundation under grant no. DMS-9101715. The government has certain rights to this material.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 B. Simon and G. Stolz