Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators
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- by David Damanik and Dirk Hundertmark PDF
- Proc. Amer. Math. Soc. 132 (2004), 1957-1962
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.References
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Additional Information
- David Damanik
- Affiliation: Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 621621
- 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
- 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
- © Copyright 2004 by the authors
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1957-1962
- MSC (2000): Primary 34L05, 47E05, 81Q10
- DOI: https://doi.org/10.1090/S0002-9939-04-06985-0
- MathSciNet review: 2053966