Pure point diffraction and mean, Besicovitch and Weyl almost periodicity

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Title

Pure point diffraction and mean, Besicovitch and Weyl almost periodicity

Author(s) or Creator(s)
Lenz, Daniel
Spindeler, Timo
Strungaru, Nicolae
Date

2020

Peer Reviewed?

No

Keywords

almost periodic measures
pure point diffraction

Description

We show that a translation bounded measure has pure point diffraction if and only if it is mean almost periodic. We then go on and show that a translation bounded measure solves what we call the phase problem if and only if it is Besicovitch almost periodic. Finally, we show that a translation bounded measure solves the phase problem independent of the underlying van Hove sequence if and only if it is Weyl almost periodic. These results solve fundamental issues in the theory of pure point diffraction and answer questions of Lagarias.

Publication Information

Lenz, D., Spindeler, T., & Strungaru, N. (2020). Pure point diffraction and mean, Besicovitch and Weyl almost periodicity. arXiv:2006.10821v1. https://arxiv.org/abs/2006.10821

Type of Item

Reports

Language

English

Location

https://roam.macewan.ca/islandora/object/gm:2708

Rights

All Rights Reserved

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