RESEARCH ARTICLE

Absence of eigenvalues for quasiperiodic Schrödinger type operators

  • Jiahao XU ,
  • Xin ZHAO
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  • Department of Mathematical Sciences, Nanjing University, Nanjing 210093, China

Received date: 10 Nov 2018

Accepted date: 27 May 2019

Published date: 15 Jun 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

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.

Cite this article

Jiahao XU , Xin ZHAO . Absence of eigenvalues for quasiperiodic Schrödinger type operators[J]. Frontiers of Mathematics in China, 2019 , 14(3) : 645 -659 . DOI: 10.1007/s11464-019-0773-9

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