Communications in Mathematical Physics

, Volume 195, Issue 1, pp 1–14

Anderson Localization for the Almost Mathieu Equation, III. Semi-Uniform Localization, Continuity of Gaps, and Measure of the Spectrum

  • Svetlana Y. Jitomirskaya
  • Yoram Last

DOI: 10.1007/s002200050376

Cite this article as:
Jitomirskaya, S. & Last, Y. Comm Math Phys (1998) 195: 1. doi:10.1007/s002200050376

Abstract:

We show that the almost Mathieu operator, \(\), has semi-uniform (and thus dynamical) localization for λ > 15 and a.e. ω,θ. We also obtain a new estimate on gap continuity (in ω) for this operator with λ > 29 (or λ < 4/29), and use it to prove that the measure of its spectrum is equal to \(\) for λ in this range and all irrational ω's.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Svetlana Y. Jitomirskaya
    • 1
  • Yoram Last
    • 2
  1. 1.Department of Mathematics, University of California, Irvine, CA 92697, USAUS
  2. 2.Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena,¶CA 91125, USAUS

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