 00227 David Damanik and Rowan Killip
 Reflection symmetries of almost periodic functions
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May 16, 00

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Abstract. We study global reflection symmetries of almost periodic functions. In the nonlimit periodic case, we establish an upper bound on the Haar measure of the set of those elements in the hull which are almost symmetric about the origin. As an application of this result we prove that in the nonlimit periodic case, the criterion of Jitomirskaya and Simon ensuring absence of eigenvalues for almost periodic Schr\"odinger operators is only applicable on a set of zero Haar measure. We complement this by giving examples of limit periodic functions where the JitomirskayaSimon criterion can be applied to every element of the hull.
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