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Absolute continuity of the spectrum of two-dimensional Schrödinger operator with partially periodic coefficients


Author: N. Filonov
Translated by: the author
Original publication: Algebra i Analiz, tom 29 (2017), nomer 2.
Journal: St. Petersburg Math. J. 29 (2018), 383-398
MSC (2010): Primary 47F05, 58J50
DOI: https://doi.org/10.1090/spmj/1498
Published electronically: March 12, 2018
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Abstract: On the plane, the operator $ -\mathrm {div} (g(x)\nabla \, \cdot \,)+V(x)$ is considered. The absolute continuity of its spectrum is proved under the assumption that each coefficient is the sum of a $ \mathbb{Z}^2$-periodic term and a summand that is periodic in one of the variables and decays superexponentially with respect to the other variable.


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Additional Information

N. Filonov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: filonov@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1498
Keywords: Schr\"odinger operator, partially periodic coefficients, absolute continuity of the spectrum
Received by editor(s): October 1, 2016
Published electronically: March 12, 2018
Additional Notes: Supported by RFBR (grant no. 14-01-00760). A part of this work was done in the Isaac Newton Institute, Cambridge, in the framework of the program “Periodic and Ergodic Spectral Problems”, EPSRC grant EP/K032208/1. The author thanks the Newton Institute for hospitality and Simons Foundation for support.
Dedicated: To the memory of V. S. Buslaev
Article copyright: © Copyright 2018 American Mathematical Society

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