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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2104.06812 |
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Table of Contents:
- Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $\RR^d$. In particular, we classify all periodic eigenmeasures on $\RR$, which gives an interesting connection with the discrete Fourier transform and its eigenvectors, as well as all eigenmeasures on $\RR$ with uniformly discrete support. An interesting subclass of the latter emerges from the classic cut and project method for aperiodic Meyer sets. Finally, we construct a large class of eigenmeasures with locally finite support that is not uniformly discrete and has large gaps around $0$.