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Absence of eigenvalues for quasiperiodic Schrödinger type operators

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Abstract

We obtain the matrix-valued Schrödinger-type operators [Hα,θ] with Lipschitz potentials having no eigenvalues on the set {E: L(E) < δC, d(α, θ)}, where δ is an explicit function depending on the sampling function C(θ), dimension d, phase θ, and frequency α, and L(E) is the Lyapunov exponent.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Nanjing University, Nanjing, 210093, China

    Jiahao Xu & Xin Zhao

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  1. Jiahao Xu
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  2. Xin Zhao
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Correspondence to Xin Zhao.

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Xu, J., Zhao, X. Absence of eigenvalues for quasiperiodic Schrödinger type operators. Front. Math. China 14, 645–659 (2019). https://doi.org/10.1007/s11464-019-0773-9

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  • DOI: https://doi.org/10.1007/s11464-019-0773-9

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