Frank, Rupert L. and Larson, Simon (2021) Discrete Schrödinger operators with decaying and oscillating potentials. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20211018-185252726
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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.
| Item Type: | Report or Paper (Discussion Paper) | ||||||||||
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| 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. | ||||||||||
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| Record Number: | CaltechAUTHORS:20211018-185252726 | ||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20211018-185252726 | ||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 111527 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | George Porter | ||||||||||
| Deposited On: | 15 Nov 2021 20:59 | ||||||||||
| Last Modified: | 15 Nov 2021 20:59 |
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