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

Filonov, N.

doi:10.1090/spmj/1498

Absolute continuity of the spectrum of two-dimensional Schrödinger operator with partially periodic coefficients
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by N. Filonov
Translated by: the author

St. Petersburg Math. J. 29 (2018), 383-398

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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