Published November 15, 2021
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Discrete Schrödinger operators with decaying and oscillating potentials
- Creators
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Frank, Rupert L.
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Larson, Simon
Abstract
We study a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential V(n) = λn^(−α) cos(πωn^β), with 1 < β < 2α, we prove that the spectrum is purely absolutely continuous on the spectrum of the Laplacian.
Additional Information
© 2021 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Partial support through U.S. National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.), through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868 (R.L.F.), and through Knut and Alice Wallenberg Foundation grant KAW 2018.0281 (S.L.) is acknowledged. In memory of Sergey Naboko.Attached Files
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Additional details
- Eprint ID
- 111527
- Resolver ID
- CaltechAUTHORS:20211018-185252726
- DMS-1363432
- NSF
- DMS-1954995
- NSF
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft (DFG)
- KAW 2018.0281
- Knut and Alice Wallenberg Foundation
- Created
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2021-11-15Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field