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Reflection Symmetries of Almost Periodic Functions

✍ Scribed by David Damanik; Rowan Killip

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
109 KB
Volume
178
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 non-limit periodic case, the criterion of Jitomirskaya and Simon ensuring absence of eigenvalues for almost periodic Schro dinger 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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