Moebius Schrödinger

  • Jean BourgainEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)


Consider the one-dimensional lattice Schrödinger operator with potential given by the Moebius function. It is shown that the Lyapounov exponent is strictly positive for almost all energies, answering a question posed by P. Sarnak.


Moebius Function Lyapounov Exponents Pointwise Closure Fubini Argument Banach Limit 
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The author is grateful to P. Sarnak for bringing the problem to his attention and several discussions. He also thanks H. Krüger for comments on how Theorem 1 in this note may be derived directly from Lemma 2 and the results in [2]. The author was partially supported by NSF Grants DMS-0808042 and DMS 0835373.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA

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