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Discrete Schrödinger operators with decaying and oscillating potentials

Frank, Rupert L. and Larson, Simon (2021) Discrete Schrödinger operators with decaying and oscillating potentials. . (Unpublished)

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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)
Related URLs:
URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Larson, Simon0000-0002-0057-8211
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.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)EXC-2111-390814868
Knut and Alice Wallenberg FoundationKAW 2018.0281
Record Number:CaltechAUTHORS:20211018-185252726
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111527
Deposited By: George Porter
Deposited On:15 Nov 2021 20:59
Last Modified:15 Nov 2021 20:59

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