On eigenmeasures under Fourier transform
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909174760210432 |
|---|---|
| author | Baake, Michael Spindeler, Timo Strungaru, Nicolae |
| author_facet | Baake, Michael Spindeler, Timo Strungaru, Nicolae |
| 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 $0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_06812 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On eigenmeasures under Fourier transform Baake, Michael Spindeler, Timo Strungaru, Nicolae Spectral Theory 42A38, 52C23 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 $0$. |
| title | On eigenmeasures under Fourier transform |
| topic | Spectral Theory 42A38, 52C23 |
| url | https://arxiv.org/abs/2104.06812 |