JournalsowrVol. 9 / No. 2DOI 10.4171/owr/2012/17

Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators

  • Artur Avila

    Université Pierre et Marie Curie, Paris, France
  • David Damanik

    Rice University, Houston, United States
  • Svetlana Jitomirskaya

    University of California, Irvine, United States
Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators cover

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Abstract

This Arbeitsgemeinschaft discussed the spectral properties of quasi-periodic Schrödinger operators in one space dimension. After presenting background material on Schrödinger operators with dynamically defined potentials and some results about certain classes of dynamical systems, the recently developed global theory of analytic one-frequency potentials was discussed in detail. This was supplemented by presentations on an important special case, the almost Mathieu operator, and results showing phenomena exhibited outside the analytic category.