Reflection symmetries of almost periodic functions
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 Schrödinger 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2000
 arXiv:
 arXiv:mathph/0005018
 Bibcode:
 2000math.ph...5018D
 Keywords:

 Mathematical Physics;
 Mathematics  Functional Analysis;
 42A75;
 43A60;
 81Q10
 EPrint:
 6 pages