Communications in Mathematical Physics

, Volume 149, Issue 2, pp 347–360 | Cite as

On the measure of gaps and spectra for discrete 1D Schrödinger operators



We study the lebesgue measure of gaps and spectra, of ergodic Jacobi matrices. We show that: |σ/A|+|G|≥v, where: σ is the spectrum,G is the union of the gaps,A is the set of energies where the Lyaponov exponent vanishes andv is an appropriate seminorm of the potential. We also study in more detail periodic Jacobi matrices, and obtain a lower bound and large coupling asymptotics for the measure of the spectrum. We apply the results of the periodic case, to limit periodic Jacobi matrices, and obtain sufficient conditions for |G|≥v and for |σ|>0.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Lebesgue Measure 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Y. Last
    • 1
  1. 1.Department of PhysicsTechnion-Israel Institute of TechnologyHaifaIsrael

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