Which Meyer sets are regular model sets? A characterization via almost periodicity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913567344689152 |
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| author | Lenz, Daniel Richard, Christoph Strungaru, Nicolae |
| author_facet | Lenz, Daniel Richard, Christoph Strungaru, Nicolae |
| contents | In 2012, Meyer introduced the notions of generalized almost periodic measure and almost periodic pattern and proved that regular model sets in Euclidean space are almost periodic patterns. Here, we prove the converse in a slightly more general setting. Specifically, we show that a Meyer set in any $σ$-compact locally compact abelian group is a regular model set if and only if it is an almost periodic pattern. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Which Meyer sets are regular model sets? A characterization via almost periodicity Lenz, Daniel Richard, Christoph Strungaru, Nicolae Mathematical Physics Classical Analysis and ODEs Dynamical Systems In 2012, Meyer introduced the notions of generalized almost periodic measure and almost periodic pattern and proved that regular model sets in Euclidean space are almost periodic patterns. Here, we prove the converse in a slightly more general setting. Specifically, we show that a Meyer set in any $σ$-compact locally compact abelian group is a regular model set if and only if it is an almost periodic pattern. |
| title | Which Meyer sets are regular model sets? A characterization via almost periodicity |
| topic | Mathematical Physics Classical Analysis and ODEs Dynamical Systems |
| url | https://arxiv.org/abs/2410.22536 |