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We consider a one-dimensional discrete Schrödinger operator whose potential has the form . Here is the projection of on , and the function is Borel measurable. We show that if the frequency vector is Liouville (the sequence has a subsequence converging to fast enough), then for Lebesgue almost every the point spectrum of the operator is empty.
Cite this article
Alexander Y. Gordon, Discrete Schrödinger operators with potentials defined by measurable sampling functions over Liouville torus rotations. J. Fractal Geom. 4 (2017), no. 4 pp. 329–337