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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Bounded eigenfunctions
and absolutely continuous spectra
for one-dimensional Schrödinger operators

Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 124 (1996), 3361-3369
MSC (1991): Primary 34L40
MathSciNet review: 1350963
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Abstract: We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann's result that potentials of bounded variation have strictly a.c. spectrum on a half-axis.

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Additional Information

Barry Simon
Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 253-37, Pasadena, California 91125

Received by editor(s): April 3, 1995
Received by editor(s) in revised form: April 24, 1995
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 Barry Simon