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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2411.14987 |
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| _version_ | 1866917845248507904 |
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| author | Feichtinger, Hans G. Richard, Christoph Schumacher, Christoph Strungaru, Nicolae |
| author_facet | Feichtinger, Hans G. Richard, Christoph Schumacher, Christoph Strungaru, Nicolae |
| contents | Mathematical diffraction theory has been developed since about 1995. Hof's initial approach relied on tempered distributions in euclidean space. Nowadays often the Fourier theory by Argabright and Gil de Lamadrid is used, which applies to appropriate measures on locally compact abelian groups. We review diffraction theory using Wiener amalgams as test function spaces. For translation bounded measures, this unifies and simplifies the former two approaches. We treat weighted versions of Meyer's model sets as examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twice Fourier transformable measures and diffraction theory Feichtinger, Hans G. Richard, Christoph Schumacher, Christoph Strungaru, Nicolae Mathematical Physics 43A07, 52C23, 43A60, 78A45 Mathematical diffraction theory has been developed since about 1995. Hof's initial approach relied on tempered distributions in euclidean space. Nowadays often the Fourier theory by Argabright and Gil de Lamadrid is used, which applies to appropriate measures on locally compact abelian groups. We review diffraction theory using Wiener amalgams as test function spaces. For translation bounded measures, this unifies and simplifies the former two approaches. We treat weighted versions of Meyer's model sets as examples. |
| title | Twice Fourier transformable measures and diffraction theory |
| topic | Mathematical Physics 43A07, 52C23, 43A60, 78A45 |
| url | https://arxiv.org/abs/2411.14987 |