Reflection symmetries of almost periodic functions

Details Reflection symmetries of almost periodic functions Reflection symmetries of almost periodic functions

2000-05-16

arxiv.org/abs/math-ph/0005018v1

Physics

Mathematical Physics

6 pages

Scientific paper

We study global reflection symmetries of almost periodic functions. In the non-limit 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 non-limit 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 Jitomirskaya-Simon criterion can be applied to every element of the hull.

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