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

 

Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators


Authors: David Damanik and Dirk Hundertmark
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1957-1962
MSC (2000): Primary 34L05, 47E05, 81Q10
Published electronically: February 26, 2004
MathSciNet review: 2053966
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Abstract: We prove a criterion for absence of decaying solutions for one-dimensional Schrödinger operators. As necessary input, we require infinitely many centers of local reflection symmetry and upper and lower bounds for the traces of the associated transfer matrices.


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Additional Information

David Damanik
Affiliation: Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125
Email: damanik@its.caltech.edu

Dirk Hundertmark
Affiliation: Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61801
Email: dirkh@caltech.edu, dirk@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-06985-0
PII: S 0002-9939(04)06985-0
Keywords: Schr\"odinger operators, eigenvalue problem, local reflection symmetries
Received by editor(s): July 3, 2002
Received by editor(s) in revised form: August 1, 2002
Published electronically: February 26, 2004
Additional Notes: Supported in part by NSF grant DMS-0010101
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 by the authors