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| The set GR of generalized reflectionless Schroedinger potentials was introduced and studied by Lundina in 1985. It contains the classical reflectionless potentials and (translations of) the algebro-geometric potentials. The class GR has been studied further by Marchenko, Gesztesy, Kotani and other scientists.
The stationary ergodic elements of GR are of interest for several reasons. It seems that all such elements which have been constructed till now are Bohr almost periodic. Our goal is to construct stationary ergodic, generalized reflectionless potentials which are almost automorphic in the sense of Bochner-Veech, but not almost periodic. To do so, we make systematic use of results concerning Parreau-Widom domains by Sodin-Yuditskii and by Hasumi. |
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